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Abstract
We consider a simple random walk on Z _{d} started at the origin and stopped on its first exit time from {equation presented}. Write L in the form L = mN with m = m(N) and N an integer going to infinity in such a way that L ^{2} ∼ AN ^{d} for some real constant A > 0. Our main result is that for d ≥ 3, the projection of the stopped trajectory to the Ntorus locally converges, away from the origin, to an interlacement process at level Adσ _{1}, where σ _{1} is the exit time of a Brownian motion from the unit cube (1, 1) ^{d} that is independent of the interlacement process. The above problem is a variation on results of Windisch (2008) and Sznitman (2009).
Original language  English 

Pages (fromto)  354388 
Number of pages  35 
Journal  Advances in Applied Probability 
Volume  56 
Issue number  1 
Early online date  24 Aug 2023 
DOIs  
Publication status  Published  24 Mar 2024 
Bibliographical note
Funding Information:The research of M. Sun was supported by an EPSRC doctoral training grant to the University of Bath with project reference EP/N509589/1/2377430.
Funding
Funders  Funder number 

Engineering and Physical Sciences Research Council  
University of Bath  EP/N509589/1/2377430 
University of Bath 
Keywords
 Interlacement
 Keywords:
 hashing
 hitting probability
 looperased random walk
ASJC Scopus subject areas
 Applied Mathematics
 Statistics and Probability
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 1 Finished

Maths Research Associates 2021
Milewski, P. (PI)
Engineering and Physical Sciences Research Council
1/10/21 → 30/06/24
Project: Research council