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Discrete mathematical modelling seminar
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2025/05/02
16:45-17:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Anton Dzhamay (BIMSA, Beijing)
On a positivity property of a solution of discrete Painlevé equations (English)
Anton Dzhamay (BIMSA, Beijing)
On a positivity property of a solution of discrete Painlevé equations (English)
[ Abstract ]
We consider a particular example of a discrete Painlevé equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich. Observing that this equation corresponds to a very special choice of parameters (root variables) in the Space of Initial Conditions for the differential Painlevé V equation, we show that some explicit special function solutions, written in terms of modified Bessel functions, for d-PV, yield the unique positive solution for some initial value problem for the discrete Painlevé equation needed for quantum minimal surfaces. This is a joint work with Peter Clarkson, Andy Hone, and Ben Mitchell.
We consider a particular example of a discrete Painlevé equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich. Observing that this equation corresponds to a very special choice of parameters (root variables) in the Space of Initial Conditions for the differential Painlevé V equation, we show that some explicit special function solutions, written in terms of modified Bessel functions, for d-PV, yield the unique positive solution for some initial value problem for the discrete Painlevé equation needed for quantum minimal surfaces. This is a joint work with Peter Clarkson, Andy Hone, and Ben Mitchell.
