The lace expansion for self interacting RW: Aussois mini course

Mark Holmes

Description

The lace expansion for self-interacting RW: Aussois mini course. Mark Holmes (Joint work with Remco v.d. Hofstad) June 2009

• course includes


• translation invariant


• interacting rw


• starting point


• rw path ?n


• self

Sujets

• Holmes
• Translational symmetry

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 39
• Langue: English

Extrait

The

lace

expansion for self-interacting Aussois mini course.

(Joint work

Mark Holmes with Remco v.d.

June 2009

Hofstad)

RW:

Thanks

and

ap

ologies:

This

mini-course includes:





an intro. to a particular method for RW

some applications of that method

studying

self-interacting

This

mini-course is not:





a survey of known results on RWRE, cookie RW or any RW models

going to answer all your questions about RW models

other

Self-interacting random walks:

 A n.n. RW pathη n is a sequence{η i } in =0 for which η i = (η [ i 1] , . . . ,η [d i ] )∈Z d and|η i+1 −η i |=1 for eachi.   Notation:p η i (y,x)is conditional probability that the walk steps fromη i =ytox, given the historyη i = (η 0 , . . . ,η i ). 

n−1 Q(X n = (x 0 ,x 1 , . . . ,x n )) =  p x i (x i ,x i+1 ).  i=0  Qassumed to be translation invariant w.r.t. point. starting

Self-interacting random walks include:









simple random walk

annealed RWRE

reinforced random walks

(annealed) cookie random

walks