One-day Workshop on Asymptotic and Potential Analysis of Stochastic Processes

• Date: August 17, 2017, 10:00 - 16:50
• Venue: Room B301, Faculty of Science Building B, Kobe University（神戸大学理学部B棟3階B301号室）
  Transportation and maps (English)　交通案内と周辺地図（日本語）
  To go to Room B301, please go upstairs from the main entrance of Building B to the 3rd floor and then turn right.
  （B301号室はB棟入口脇にある階段を上がり，そこから右に進んだところにあります．）
• Organizer: Naotaka Kajino (Kobe University)

Program

• 10:00 - 10:50　KUBOTA, Naoki (Nihon University)
  Continuity results for the frog model in random initial configurations
• 11:10 - 12:00　NAMBA, Ryuya (Okayama University)
  Central limit theorems for non-symmetric random walks on nilpotent covering graphs

• 13:20 - 14:20　ANDRES, Sebastian (University of Cambridge)
  Diffusion processes on branching Brownian motion
• 14:40 - 15:30　MATSUURA, Kouhei (Tohoku University)
  Compactness of Brownian semigroups associated with Robin boundary condition
• 15:50 - 16:40　ABE, Yoshihiro (Kobe University)
  Second order term of cover time for planar simple random walk

Abstracts

• KUBOTA, Naoki (Nihon University)
  Continuity results for the frog model in random initial configurations
  We consider the frog model in random initial configurations. The dynamics of this model is as
  follows: Assign randomly simple random walks to sites of the multidimensional cubic lattice,
  and these simple random walks are regarded as ``frogs.'' Suppose that at least one frog exists
  at the origin and only frogs sitting on the origin are active (the other frogs are sleeping and do
  not move at first). When sleeping frogs are attacked by an active one, those become active and
  start moving. Then, a fundamental object of study is the first passage time at which an active
  frog reaches a site. It is known that this first passage time is asymptotically equal to the so-called
  time constant, which depends on the law of the random initial configuration. In this talk we present
  the continuity for the time constant with respect to the law of the random initial configuration.


• NAMBA, Ryuya (Okayama University)
  Central limit theorems for non-symmetric random walks on nilpotent covering graphs
  The long time asymptotics for random walks on infinite graphs is a principal topic for both
  geometers and probabilists. A covering graph of a finite graph with a nilpotent covering
  transformation group is called a nilpotent covering graph, regarded as a generalization of
  a crystal lattice or the Cayley graph of a finite generated group of polynomial growth. We
  discuss non-symmetric random walks on nilpotent covering graphs from a view point of the
  theory of discrete geometric analysis developed by Kotani and Sunada. Our main purpose of
  this talk is to give a functional central limit theorem for them. We also discuss an example of
  non-symmetric random walks on nilpotent covering graphs with several figures and animations.
  This talk is based on joint work with Satoshi Ishiwata (Yamagata University) and Hiroshi Kawabi
  (Okayama University).


• ANDRES, Sebastian (University of Cambridge)
  Diffusion processes on branching Brownian motion
  Branching Brownian motion (BBM) is a classical process in probability, describing a population
  of particles performing independent Brownian motion and branching according to a Galton
  Watson process. In this talk we present a one-dimensional diffusion process on BBM particles
  which is symmetric with respect to a certain random martingale measure. This process is obtained
  by a time-change of a standard Brownian motion in terms of the associated positive continuous
  additive functional. In a sense it may be regarded as an analogue of Liouville Brownian motion
  which has been recently constructed in the context of a Gaussian free field. This is joint work
  with Lisa Hartung (New York University).


• MATSUURA, Kouhei (Tohoku University)
  Compactness of Brownian semigroups associated with Robin boundary condition
  In this talk, we consider the first order $L^2$-Sobolev space with Robin boundary condition.
  Moreover, we give a sufficient condition for the semigroup associated with this space is an
  $L^2$-compact operator.


• ABE, Yoshihiro (Kobe University)
  Second order term of cover time for planar simple random walk
  I will consider the cover time for a simple random walk on the two-dimensional discrete
  torus of side length n. Dembo-Peres-Rosen-Zeitouni (2004) identified the leading term in
  the asymptotics for the cover time as n goes to infinity. I will talk about the exact second
  order term. This is a discrete analogue of the work on the cover time for planar Brownian
  motion by Belius and Kistler (2017).

• JSPS Grant-in-Aid for Young Scientists (B) Grant Number 15K17554
  「特異的幾何学構造に由来する微分作用素とその確率論的対応物に対する数学解析」
  (Principal Investigator: Naotaka Kajino (Department of Mathematics, Kobe University))

Naotaka Kajino
Department of Mathematics, Graduate School of Science, Kobe University,
Rokkodai-cho 1-1, Nada-ku, 657-8501 Kobe, Japan
Office: Faculty of Science Building B, Room B426
Tel: +81-78-803-5616
Fax: +81-78-803-5610
E-mail: nkajino ``at" math.kobe-u.ac.jp