Probabilistic methods in geometry, topology, and spectral theory /

This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22-26, 2016 and Probabilistic Methods in Topology, held from November 14-18, 2016 at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec,...

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Bibliographic Details
Call Number:Libro Electrónico
Other Authors: Canzani, Yaiza, 1987- (Editor), Chen, Linan, 1984- (Editor), Jakobson, Dmitry, 1970- (Editor)
Format: Electronic eBook
Language:Inglés
Published: Providence, Rhode Island : Montreal, Quebec, Canada : American Mathematical Society ; Centre de Recherches Mathematiques, 2019.
Series:Contemporary mathematics, volume 739
Subjects:
Mathematical physics > Congresses.
Probabilities > Congresses.
Geometric analysis > Congresses.
Topology > Congresses.
Spectral theory (Mathematics) > Congresses.
Physique mathématique > Congrès.
Probabilités > Congrès.
Analyse géométrique > Congrès.
Topologie > Congrès.
Spectre (Mathématiques) > Congrès.
Topología
Procesos estocásticos
Recorridos aleatorios (Matemáticas)
Geometric analysis
Mathematical physics
Probabilities
Spectral theory (Mathematics)
Topology
Combinatorics {For finite fields, see 11Txx} > Graph theory {For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15} > Random graphs [See also 60B20].
Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for.
Partial differential equations > Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05] > Asymptotic distribution of eigenvalues and eigenfunctions.
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} > Partial differential equations on manifolds; differential op.
Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} > Combinatorial probability > Combinatorial probability.
Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} > Stochastic processes > Gaussian processes.
Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} > Stochastic processes > Random fields.
Quantum theory > General mathematical topics and methods in quantum theory > Quantum chaos [See also 37Dxx].
Conference papers and proceedings
Online Access:Texto completo
Table of Contents:
  • Cover; Title page; Contents; Preface; A geometric treatment of log-correlated Gaussian free fields; 1. Introduction; 2. Abstract Wiener Space and Gaussian Free Fields; 3. Regularization of GFF on ℝⁿ; 4. Random Measure and KPZ in ℝ³; References; Tangent nodal sets for random spherical harmonics; 1. Introduction; 2. Geometric Preliminaries; 3. Calculating the Expectation; Appendix A. Computation of Covariance Matrix; References; Formal Zeta function expansions and the frequency of Ramanujan graphs; 1. Introduction; 2. Main Results; 3. Graph Theoretic Preliminaries; 3.1. Graphs and Morphisms
  • 4. Variants of the Zeta Function5. The Expected Value of \cL_{ }; 6. A Simpler Variant of the ᵢ and \cPᵢ; 7. Random Graph Covering Maps and Other Models; 8. Numerical Experiments; References; Rank and Bollobás-Riordan polynomials: Coefficient measures and zeros; 1. Introduction; 2. Tutte polynomial; 3. Distribution of the coefficients: a priori results; 4. Numerical experiments on the coefficient measure; 5. Zeros of Tutte polynomials; 6. Ribbon graphs: summary; 7. Ribbon graphs and "left-hand turn" surfaces; 8. Bollobás-Riordan polynomials; 9. Random graphs with orientations
  • 10. Convergence of the coefficient measures of Bollobás-Riordan polynomials11. Numerical investigations: coefficients and zeros of Bollobás-Riordan polynomials; 12. Conclusion; Appendix: Computer code; Acknowledgements; References; The Brownian motion on (ℝ) and quasi-local theorems; 1. Introduction; 2. Diffusion on \Aff(\R) and similar groups; 3. Approximation of diffusion by random walks and associated return probability estimates; 4. Quasi-Local Theorems; Acknowledgments; References; Quantum limits of Eisenstein series in ℍ³; 1. Introduction; 2. Spectral Theory in \pslok\\uphs
  • 3. ProofsReferences; Observability and quantum limits for the Schrödinger equation on ^{ }; 1. Introduction; 2. Statement of the main results; 3. Semiclassical measures and their invariance properties; Acknowledgments; References; Random nodal lengths and Wiener chaos; 1. Introduction; 2. Random nodal lengths; 3. Chaotic expansions; 4. On the proof of Theorem 2.2; 5. Further related work; Acknowledgments; References; Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras; 1. Introduction; 2. Notation; 3. Bounds on the mass of tubes
  • 4. Diophantine Lemmata5. Bounds on the mass of tubes, II; 6. The AQUE problem and the application of the entropy bound.; Appendix A. Proof of Lemma A.1: how to construct a higher rank amplifier; Acknowledgments; References; Back Cover

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