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Tokyo Probability Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima |
2016/07/11
15:00-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Jin Feng (University of Kansas) 15:00-16:30
An introduction to Hamilton-Jacobi equation in the space of probability measures (English)
Jin Feng (University of Kansas) 15:00-16:30
An introduction to Hamilton-Jacobi equation in the space of probability measures (English)
[ Abstract ]
I will discuss Hamilton-Jacobi equation in the space of probability measures.
Two types of applications motivate the issue: one is from the probabilistic large deviation study of weakly interacting particle systems in statistical mechanics, another is from an infinite particle version of the variational formulation of Newtonian mechanics.
In creating respective well-posedness theories, two mathematical observations played important roles: One, the free-particle flow picture naturally leads to the use of the optimal mass transportation calculus. Two, there is a hidden symmetry (particle permutation invariance) for elements in the space of probability measures. In fact, the space of probability measures in this context is best viewed as an infinite dimensional quotient space. Using a natural metric, we are lead to some fine aspects of the optimal transportation calculus that connect with the metric space analysis and probability.
Time permitting, I will discuss an open issue coming up from the study of the Gibbs-Non-Gibbs transitioning by the Dutch probability community.
The talk is based on my past works with the following collaborators: Markos Katsoulakis, Tom Kurtz, Truyen Nguyen, Andrzej Swiech and Luigi Ambrosio.
Daishin Ueyama (Graduate School of Advanced Mathematical Sciences, Meiji University) 16:50-18:20I will discuss Hamilton-Jacobi equation in the space of probability measures.
Two types of applications motivate the issue: one is from the probabilistic large deviation study of weakly interacting particle systems in statistical mechanics, another is from an infinite particle version of the variational formulation of Newtonian mechanics.
In creating respective well-posedness theories, two mathematical observations played important roles: One, the free-particle flow picture naturally leads to the use of the optimal mass transportation calculus. Two, there is a hidden symmetry (particle permutation invariance) for elements in the space of probability measures. In fact, the space of probability measures in this context is best viewed as an infinite dimensional quotient space. Using a natural metric, we are lead to some fine aspects of the optimal transportation calculus that connect with the metric space analysis and probability.
Time permitting, I will discuss an open issue coming up from the study of the Gibbs-Non-Gibbs transitioning by the Dutch probability community.
The talk is based on my past works with the following collaborators: Markos Katsoulakis, Tom Kurtz, Truyen Nguyen, Andrzej Swiech and Luigi Ambrosio.
