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Exponential functionals of two random walks and stationary measures of discrete growth processes
Abstract
We study random walks with geometric or log-gamma increments, reweighted by certain exponential functionals. We establish precise asymptotics for all moments of exponential functionals, revealing a phase transition as the drifts of the walks vary. To describe the large time limit of reweighted random walks, we introduce a discrete T transformation on random walk paths and establish Girsanov relations. As a corollary, we show that the stationary measures of geometric last passage percolation and the log-gamma polymer on a strip converge to their half-space counterparts as the strip width tends to infinity. In the log-gamma case, this provides an alternative proof of a recent result in arXiv:2607.17030.
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BibTeX
@misc{ouyang2026exponential,
title = {{Exponential functionals of two random walks and stationary measures of discrete growth processes}},
author = {Zikun Ouyang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19673},
eprint = {2610.19673},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19673},
}
RIS
TY - UNPB
TI - Exponential functionals of two random walks and stationary measures of discrete growth processes
AU - Zikun Ouyang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19673
UR - https://arxiv.org/abs/2610.19673
AB - We study random walks with geometric or log-gamma increments, reweighted by certain exponential functionals. We establish precise asymptotics for all moments of exponential functionals, revealing a phase transition as the drifts of the walks vary. To describe the large time limit of reweighted random walks, we introduce a discrete T transformation on random walk paths and establish Girsanov relations. As a corollary, we show that the stationary measures of geometric last passage percolation and the log-gamma polymer on a strip converge to their half-space counterparts as the strip width tends to infinity. In the log-gamma case, this provides an alternative proof of a recent result in arXiv:2607.17030.
ER -