Elliptic Dyson Models Makoto Katori (Chuo Univ., Tokyo)

Tuesday, March 21, 2017

Workshop on

`Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics’

March 20-24, 2017 ESI, Boltzmann Lecture Hall

University of Vienna 1

Plan of my talk 1. Introduction Martingales and 1-dim. Brownian Motion Complex BM and Conformal Invariance Entire Functions and Determinantal Martingale Determinantal Measures and Processes Problem 2. Results Theorem 1, Theorem 2 3. Key Lemmas and Open Problems

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1. Introduction

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Martingales and 1-dim. Brownian Motion

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Complex BM and Conformal Invariance

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Entire Functions and Det. Martingale

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Determinantal Measures and Processes

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Proposition 1

Problem

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?

2. Results

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Theorem 1

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Theorem 2

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3. Key Lemmas and Open Problems

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A Key Lemma for Theorem 1

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Lemma 1

A Key Lemma for Theorem 2

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A Key Lemma for Theorem 2

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Lemma 2

Open Problem 1

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Open Problem 2

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Thank you very much for your attention.

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A Lecture Note entitled `Bessel Processes, Schramm-Loewner Evolution,

and the Dyson Model’ was published (2016) as

SpringerBriefs in Mathematical Physics 11