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Author : Maurice Duits
Publisher :
ISBN 13 : 9781470448219
Total Pages : pages
Book Rating : 4.4/5 (482 download)
Download or read book On Mesoscopic Equilibrium for Linear Statistics in Dyson's Brownian Motion written by Maurice Duits and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maurice Duits
Publisher : American Mathematical Soc.
ISBN 13 : 1470429640
Total Pages : 130 pages
Book Rating : 4.4/5 (74 download)
Download or read book On Mesoscopic Equilibrium for Linear Statistics in Dyson's Brownian Motion written by Maurice Duits and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.
Author : Jun Kigami
Publisher : American Mathematical Soc.
ISBN 13 : 1470436205
Total Pages : 130 pages
Book Rating : 4.4/5 (74 download)
Download or read book Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance written by Jun Kigami and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.
Author : Sergey Bobkov
Publisher : American Mathematical Soc.
ISBN 13 : 1470436507
Total Pages : 138 pages
Book Rating : 4.4/5 (74 download)
Download or read book One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances written by Sergey Bobkov and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
Author : Andreas Seeger
Publisher : American Mathematical Soc.
ISBN 13 : 1470434377
Total Pages : 146 pages
Book Rating : 4.4/5 (74 download)
Download or read book Multilinear Singular Integral Forms of Christ-Journe Type written by Andreas Seeger and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a class of multilinear singular integral forms which generalize the Christ-Journe multilinear forms. The research is partially motivated by an approach to Bressan’s problem on incompressible mixing flows. A key aspect of the theory is that the class of operators is closed under adjoints (i.e. the class of multilinear forms is closed under permutations of the entries). This, together with an interpolation, allows us to reduce the boundedness.
Author : Nawaf Bou-Rabee
Publisher : American Mathematical Soc.
ISBN 13 : 1470431815
Total Pages : 136 pages
Book Rating : 4.4/5 (74 download)
Download or read book Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations written by Nawaf Bou-Rabee and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.
Author : Chuanqiang Chen
Publisher : American Mathematical Soc.
ISBN 13 : 1470435241
Total Pages : 94 pages
Book Rating : 4.4/5 (74 download)
Download or read book On Space-Time Quasiconcave Solutions of the Heat Equation written by Chuanqiang Chen and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.
Author : Oliver Lorscheid
Publisher : American Mathematical Soc.
ISBN 13 : 1470436477
Total Pages : 90 pages
Book Rating : 4.4/5 (74 download)
Download or read book Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces written by Oliver Lorscheid and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.
Author : Alexandru D. Ionescu
Publisher : American Mathematical Soc.
ISBN 13 : 1470431033
Total Pages : 136 pages
Book Rating : 4.4/5 (74 download)
Download or read book Global Regularity for 2D Water Waves with Surface Tension written by Alexandru D. Ionescu and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.
Author : Atanas Atanasov
Publisher : American Mathematical Soc.
ISBN 13 : 147043489X
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)
Download or read book Interpolation for Normal Bundles of General Curves written by Atanas Atanasov and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,pn. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle NC of a general nonspecial curve of degree d and genus g in Pr (with d≥g+r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H0(NC(−D))=0 or H1(NC(−D))=0), with exactly three exceptions.
Author : Paul Feehan
Publisher : American Mathematical Soc.
ISBN 13 : 147041421X
Total Pages : 254 pages
Book Rating : 4.4/5 (74 download)
Download or read book An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants written by Paul Feehan and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.
Author : Alexander Nagel
Publisher : American Mathematical Soc.
ISBN 13 : 1470434385
Total Pages : 156 pages
Book Rating : 4.4/5 (74 download)
Download or read book Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms written by Alexander Nagel and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.
Author : Laurent Lazzarini
Publisher : American Mathematical Soc.
ISBN 13 : 147043492X
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)
Download or read book Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems written by Laurent Lazzarini and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
Author : Michael Aschbacher
Publisher : American Mathematical Soc.
ISBN 13 : 1470435209
Total Pages : 194 pages
Book Rating : 4.4/5 (74 download)
Download or read book On Fusion Systems of Component Type written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups. Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.
Author : Joan Bosa
Publisher : American Mathematical Soc.
ISBN 13 : 1470434709
Total Pages : 112 pages
Book Rating : 4.4/5 (74 download)
Download or read book Covering Dimension of C*-Algebras and 2-Coloured Classification written by Joan Bosa and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors introduce the concept of finitely coloured equivalence for unital -homomorphisms between -algebras, for which unitary equivalence is the -coloured case. They use this notion to classify -homomorphisms from separable, unital, nuclear -algebras into ultrapowers of simple, unital, nuclear, -stable -algebras with compact extremal trace space up to -coloured equivalence by their behaviour on traces; this is based on a -coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, -stable -algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a “homotopy equivalence implies isomorphism” result for large classes of -algebras with finite nuclear dimension.
Author : William Goldman
Publisher : American Mathematical Soc.
ISBN 13 : 1470436140
Total Pages : 92 pages
Book Rating : 4.4/5 (74 download)
Download or read book Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane written by William Goldman and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .
Author : Arthur Bartels
Publisher : American Mathematical Soc.
ISBN 13 : 1470435233
Total Pages : 114 pages
Book Rating : 4.4/5 (74 download)
Download or read book Fusion of Defects written by Arthur Bartels and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. The authors' most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.
