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, Can...
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| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
20.11.2019
Centre de Recherches Mathematiques |
| Edition: | 1 |
| Series: | Contemporary Mathematics |
| Subjects: | |
| ISBN: | 9781470441456, 1470441454 |
| ISSN: | 0271-4132, 1098-3627 |
| Online Access: | Get full text |
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Table of Contents:
- A geometric treatment of log-correlated Gaussian free fields -- Tangent nodal sets for random spherical harmonics -- Formal Zeta function expansions and the frequency of Ramanujan graphs -- Rank and Bollobás-Riordan polynomials: Coefficient measures and zeros -- The Brownian motion on <inline-formula content-type="math/mathml"> Aff <!-- --> ( R ) \operatorname {Aff}(\mathbb {R}) </inline-formula> and quasi-local theorems -- Quantum limits of Eisenstein series in <inline-formula content-type="math/mathml"> H 3 \mathbb {H}^{3} </inline-formula> -- Observability and quantum limits for the Schrödinger equation on <inline-formula content-type="math/mathml"> S d \mathbb {S}^d </inline-formula> -- Random nodal lengths and Wiener chaos -- Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras
- 2. Spectral Theory in \pslok\\uphs -- 3. Proofs -- References -- 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 Lemmata -- 5. 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
- 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 Function -- 5. 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 polynomials -- 11. 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