with Boundary Points, Multiple SLEs, and Log-Gases arXiv: - - PowerPoint PPT Presentation

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with Boundary Points, Multiple SLEs, and Log-Gases arXiv: - - PowerPoint PPT Presentation

Sep 27, 2023 394 likes •945 views

Gaussian Free Fields with Boundary Points, Multiple SLEs, and Log-Gases arXiv: math.PR/1903.09925v2 Makoto KATORI (Chuo Univ., Tokyo) joint work with Shinji KOSHIDA (Chuo Univ.) The 12th Mathematical Society of Japan, Seasonal Institute

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Gaussian Free Fields with Boundary Points, Multiple SLEs, and Log-Gases

arXiv: math.PR/1903.09925v2

Makoto KATORI (Chuo Univ., Tokyo)

joint work with Shinji KOSHIDA (Chuo Univ.)

The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI)

Stochastic Analysis, Random Fields and Integrable Probability

Kyushu University, Fukuoka

1 August 2019

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Plan

  • 1. Introduction

1.1 Stochastic log-gases in R 1.2 Loewner equation for multi-slit 1.3 Multiple Schramm-Leowner evolution (SLE) 1.4 Gaussian free field (GFF) 1.5 Imaginary surface

  • 2. Imaginary Surface with Boundary Points (IS-BPs)
  • 3. Two Ways of Sampling IS-BPs
  • 4. Main Theorems (Theorems 4.1 and 4.2)
  • 5. Proof of Theorem 4.1
  • 6. Concluding Remarks

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  • 1. Introduction

1.1 Stochastic log-gases in R

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1.2 Loewner equation for multi-slit

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1.3 Multiple Schramm-Leowner evolution (multiple SLE)

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1.4 Gaussian free field (GFF)

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On the Green’s funciton

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1.5 Imaginary surface (IS)

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  • 2. Imaginary Surface with Boundary Points (IS-BPs)

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  • 3. Two Ways of Sampling IS-BPs
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Coupling GFF and multiple SLE

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  • 4. Main Theorems

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  • 5. Proof of Theorem 4.1

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three conditions

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Proof of Theorem 4.1

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Proof of Theorem 4.1

Dirichlet energy

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  • 6. Concluding Remarks

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Thank you very much for your attention.