| Language |
English
|
| From |
2011/03/17 15:30
|
| To |
2011/03/17 17:00
|
| Place | Room 108, Building No.3, Faculty of Science, Kyoto University |
| Seminar Name | Kansai Probability Theory Seminar |
| Title |
CLT for biased random walk on multi-type Galton-Watson tree |
| Field |
Analysis
Other
|
| Speakers | Amir Dembo |
| Affiliation | Stanford University |
| Abstract | Let T be a rooted multi-type Galton-Watson (MGW) tree of finitely many
types with at least one offspring at each vertex and an offspring
distribution with exponential tails. The r-biased random walk X(t)
on T is the nearest neighbor random walk which, when at a vertex v
with d(v) offspring, moves closer to the root with probability
r/(r+d(v)) and to each of the offspring with probability 1/(r+d(v)).
This walk is transient if and only if 0<r<R, with R the Perron-Frobenius
eigenvalue for the (assumed) irreducible matrix of expected offspring
numbers. Following the approach of Peres and Zeitouni (2008), in a joint
work with Nike Sun we show that at the critical value r=R, for almost
every T, the process |X(nt)|/sqrt(n) converges in law as n goes to
infinity to a deterministic positive multiple of a reflected Brownian
motion. Our proof is based on a new explicit description of a reversing
measure for this walk from the point of view of the particle, a
construction which extends to the reversing measure for
a biased random walk with random environment (RWRE) on MGW trees,
again at a critical value of the bias.
|
| Note | 時間、場所ともに通常と異なりますので、ご注意下さい。 |
| Link | http://www-an.acs.i.kyoto-u.ac.jp/~hino/probability/seminar/index_j.html |
|