ISSN 1881-6193

RIMS K6kyuroku Bessatsu 879

edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata,

April, 2020
Research Institute for Mathematical Sciences
Kyoto University,

RIMS Kôkyûroku Bessatsu B79

Stochastic Analysis on Large Scale Interacting Systems

November 5～8, 2018edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata,
Hirofumi Osada and Kenkichi Tsunoda

April, 2020
Research Institute for Mathematical Sciences
Kyoto University, Kyoto, Japan
The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
ⓒ2020 by the Research Institute for Mathematical Sciences, an International Joint Usage/ResearchCenter located in Kyoto University. All rights reserved. Printed in Japan.

Preface
This volume of RIMS Kôkyûroku Bessatsu is the proceedings of the RIMS workshop “Stochastic Analysis on Large Scale Interacting Systems” (SALSIS) held at
Research Institute for Mathematical Sciences, Kyoto University from November 5to 8, 2018. The workshop was held in the framework of the RIMS Joint Research(open). The SALSIS is held continuously every year starting from 2002 at diﬀerent
sites and this was the 17th workshop.
The aim of the workshop was to overview recent progress in stochastic analysison large scale interacting systems. The workshop program included 22 talks on
the problems related to interacting particle systems, the random matrix theory,random geometry, stochastic PDEs, random walks in random environments, criticalphenomena, the interface model and others. We had 41 participants during theworkshop.
This volume edited by the five organizers listed below is a collection of articles
contributed by speakers of the conference. Each paper has been carefully refereed
and is in its final form.
We would like to express our gratitude to all speakers, participants and the staﬀof the RIMS, who contributed to the great success of the workshop. We would
also like to express our sincere gratitude to the authors and the referees of thearticles of this volume for their excellent jobs in a very tight schedule. Finally,
we would like to acknowledge financial supports from the Research Institute forMathematical Sciences, an ɹ International Joint Usage/Research Center locatedin Kyoto University and JSPS KAKENHI Grant Numbers (S) 16H06338, ɹ (A)
18H03672 and (A) 17H01093.
February 2020
Ryoki Fukushima (Kyoto University)
Tadahisa Funaki (Waseda University)
Yukio Nagahata (Niigata University)
Hirofumi Osada (Kyushu University)
Kenkichi Tsunoda (Osaka University)iStochastic Analysis on Large Scale Interacting
Systems
Date: November 5 (Mon)-November 8 (Thu), 2018
Place: RIMS 420, Kyoto University
Organizers: Ryoki Fukushima (Kyoto University)
Tadahisa Funaki (Waseda University)
Yukio Nagahata (Niigata University)
Hirofumi Osada (Kyushu University)
Kenkichi Tshunoda (Osaka University)

Program
November 5 (Mon)
10:10-10:50 Tadahisa Funaki (Waseda University):
Derivations of motion by mean curvature and Stefan problem from Glauber-Kawasaki dynamics
11:10-11:50 Insuk Seo (Seoul National University):
Scaling limit of metastable random processes
13:30-14:10 Hideki Tanemura (Keio University):
Infinite particle systems with hard core and long range interactions
14:20-14:50 Yosuke Kawamoto (Kyushu University):
Transitions between dynamics of infinite particle systems associated with universal random
point fields related to random matrices
15:30-16:00 Shota Osada (Kyushu University):
Isomorphisms between determinantal point processes and Poisson point processes
16:10-16:50 Akira Sakai (Hokkaido University):
Critical two-point function for long-range models with power-law couplings: the marginal casefor d ≥ dc
November 6 (Tue)
9:20-10:00 Daisuke Shiraishi (Kyoto University):
Natural parametrization for the scaling limit of loop-erased random walk in three dimensions
10:10-10:50 David Croydon (Kyoto University):
Dynamics of the box-ball system with random initial conditions via Pitman’s transformation
11:10-11:50 Alejandro Ramı́rez (Pontificia Universidad Catolica de Chile):
Exponential decay for the exit probability from slabs of ballistic RWRE
11:50-13:30 Lunch
13:30-14:10 Tomoyuki Shirai (Kyushu University):
Universality of determinantal point processes on Riemannian manifoldsii14:20-14:50 Kazuki Okamura (Shinshu University)
Bi-infinite geodesics of first passage percolation on some infinite graphs
15:30-16:00 Naoki Kubota (Nihon University):
Continuity result for the rate function of the simple random walk on supercritical percolation
clusters
16:10-16:50 Kenkichi Tsunoda (Osaka University):
Incompressible limit for the WASEP
November 7 (Wed)
9:20-10:00 Makiko Sasada (University of Tokyo):
Hydrodynamic limit for degenerate dynamics
10:10-10:50 Sunder Sethuraman (University of Arizona):
Approximating geodesics via random points
11:00-11:40 Van Hao Can (Vietnam Academy of Science and Technology):
Sublinearity for the variance of the passage time in frog models
11:50-12:20 George Andriopoulos (University of Warwick)
Invariance principles for random walks in random environment on trees
November 8 (Thu)
9:20-10:00 Yuzuru Inahama (Kyushu University):
Paracontrolled quasi-geostrophic equation with space-time white noise
10:10-10:50 Masato Hoshino (Kyushu University):
A relation between regularity structures and paracontrolled calculus
11:10-11:50 Bin Xie (Shinshu University):
Dimension-free Harnack inequalities for the Markov semigroup generated by reflected SPDEs
11:50-13:30 Lunch
13:30-14:10 Takashi Imamura (Chiba University):
q-Whittaker measures and Schur measures
14:20-14:50 Trinh Khanh Duy (Tohoku University):
Limit theorems for Betti numbers of random geometric complexes built over binomial point
processes
15:00-15:40 Hirofumi Osada (Kyushu University):
IFC condition for infinite-dimensional stochastic diﬀerential equationsiii

Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iProgram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iiContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

Insuk Seo
Analysis of Metastable Behavior via Solutions of Poisson Equations . . .

1

Yosuke Kawamoto
Transitions of generalised Bessel kernels related to biorthogonal ensembles 19
Shota Osada
Tree representations of α-determinantal point processes . . . . . . . . . . 33
Akira Sakai
Crossover phenomena in the critical behavior for long-range models with power-law couplings . . . . . . . . . . . . . . . . . . . . . . . . . 51
David Croydon and Makiko Sasada
Duality between box-ball systems of finite box and/or carrier capacity . . 63
Ryoki Fukushima and Alejandro F. Ramı́rez
New high-dimensional examples of ballistic random walks in random environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Makoto Katori and Tomoyuki Shirai
Scaling limit for determinantal point processes on spheres . . . . . . . . . 123
Naoki Kubota
Quenched lower large deviation for the first passage time of thefrog model in random initial configurations . . . . . . . . . . . . . . . . . 139
Kenkichi Tsunoda
Hydrostatic limit for exclusion process with slow boundary revisited . . . 149
George Andriopoulos
Scaling limit of a biased random walk on a critical branchingrandom walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Masato Hoshino
Commutator estimates from a viewpoint of regularity structures . . . . . 179
Bin Xie
A note on random strings with values in a bounded convex domain . . . . 199
Khanh Duy Trinh
On persistent homology of random Čech complexesiv. . . . . . . . . . . . 215