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arXiv · 2610.19673

Exponential functionals of two random walks and stationary measures of discrete growth processes

Zikun Ouyang
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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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Zikun Ouyang. 2026-10-14. Exponential functionals of two random walks and stationary measures of discrete growth processes. https://arxiv.org/abs/2610.19673

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