Tokyo Probability Seminar

Seminar information archive ~07/20Next seminarFuture seminars 07/21~

Date, time & place Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Makiko Sasada, Shuta Nakajima

2023/11/27

17:00-18:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Stefan Junk (学習院大学)
Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)
[ Abstract ]
We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time
polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show
that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.