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Invariant measures for KdV and Toda-type discrete integrable systems Croydon, David
Description
This talk is based on joint work with Makiko Sasada (University of Tokyo) and Satoshi Tsujimoto (Kyoto University). I will give a brief introduction to four discrete integrable systems, which are derived from the KdV and Toda lattice equations, and discuss some arguments that are useful in identifying invariant measures for them. As a first key input, I will describe how it is possible to construct global solutions for each of the systems of interest using variants of Pitman's transformation. Secondly, I will present a "detailed balance" criterion for identifying i.i.d.-type invariant measures, and will relate this to approaches used to study various stochastic integrable systems, such as last passage percolation, random polymers, and higher spin vertex models. In many of the examples I discuss, solutions to the detailed balance criterion are given by well-known characterizations of certain standard distributions, including the exponential, geometric, gamma and generalized inverse Gaussian distributions. Our work leads to a number of natural conjectures about the characterization of some other standard distributions.
Item Metadata
Title |
Invariant measures for KdV and Toda-type discrete integrable systems
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-06-12T10:00
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Description |
This talk is based on joint work with Makiko Sasada (University of Tokyo) and Satoshi Tsujimoto (Kyoto University). I will give a brief introduction to four discrete integrable systems, which are derived from the KdV and Toda lattice equations, and discuss some arguments that are useful in identifying invariant measures for them. As a first key input, I will describe how it is possible to construct global solutions for each of the systems of interest using variants of Pitman's transformation. Secondly, I will present a "detailed balance" criterion for identifying i.i.d.-type invariant measures, and will relate this to approaches used to study various stochastic integrable systems, such as last passage percolation, random polymers, and higher spin vertex models. In many of the examples I discuss, solutions to the detailed balance criterion are given by well-known characterizations of certain standard distributions, including the exponential, geometric, gamma and generalized inverse Gaussian distributions. Our work leads to a number of natural conjectures about the characterization of some other standard distributions.
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Extent |
40.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Kyoto University
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Series | |
Date Available |
2020-12-12
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0395243
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International