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Title Probabilistic methods in geometry, topology, and spectral theory / Yaiza Canzani, Linan Chen, Dmitry Jakobson, editors
Published Providence, Rhode Island : American Mathematical Society ; Montreal, Quebec, Canada : Centre de Recherches Mathematiques, 2019

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Description 1 online resource
Series Contemporary mathematics, 0271-4132 ; volume 739
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
Summary 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, Canada. Probabilistic methods have played an increasingly important role in many areas of mathematics, from the study of random groups and random simplicial complexes in topology, to the theory of random Schrödinger operators in mathematical physics. The workshop on Probabilistic Methods in Spectral Ge
Notes "CRM workshop on probabilistic methods in spectral geometry and PDE, August 22-26, 2016 [and] probabilistic methods in topology, November 22-26, 2016."
Five workshops were held, August-December 2016
Bibliography Includes bibliographical references
Notes Print version record
Subject Mathematical physics -- Congresses
Probabilities -- Congresses
Geometric analysis -- Congresses
Topology -- Congresses
Spectral theory (Mathematics) -- Congresses
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].
Genre/Form Conference papers and proceedings
Form Electronic book
Author Canzani, Yaiza, 1987- editor.
Chen, Linan, 1984- editor.
Jakobson, Dmitry, 1970- editor.
ISBN 1470455994
9781470455996