Coalescence and fluctuations of O'Connellunicodex2013Yor polymers via the free-energy correlation profile
Abstract
We establish an identity relating the spatial derivative of a two-point free-energy correlation to two fundamental geometric quantities: the annealed probability that two independently sampled polymers, in the same environment, meet before reaching the prescribed terminal level, and the exit-point location of a single polymer. Our result is inspired in part by recent integration-by-parts work of Gu and Quastel for the KPZ equation. A crucial step in their continuous setting relies on an ingenious application of Itô's formula, which has no direct analogue in our semi-discrete setting. Instead, we exploit intrinsic symmetries of the polymer model together with the memoryless property. We also provide two applications: (i) we recover the horizontal Burke property by proving that the anchored stationary horizontal free-energy profile is a two-sided Brownian motion; (ii) in the zero-temperature limit, we obtain the corresponding identity for Brownian last-passage percolation.
Related
- Gao's dyadic density-one coalescence conjecture
- First pair coalescence among three geodesics
- Strong disorder and very strong disorder are equivalent for directed polymers
- Invariance in half-space last passage percolation and directed polymers
- Moments Comparison Inequalities for Critical 2d Stochastic Heat Flow, Polymers and GMC
BibTeX
@misc{rassoulagha2026coalescence,
title = {{Coalescence and fluctuations of O'Connell$\unicodex2013$Yor polymers via the free-energy correlation profile}},
author = {Firas Rassoul-Agha and Xiao Shen and Ruixuan Zhang and Guangqu Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02064},
eprint = {2609.02064},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02064},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Coalescence and fluctuations of O'Connellunicodex2013Yor polymers via the free-energy correlation profile
AU - Firas Rassoul-Agha
AU - Xiao Shen
AU - Ruixuan Zhang
AU - Guangqu Zheng
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02064
UR - https://arxiv.org/abs/2609.02064
AB - We establish an identity relating the spatial derivative of a two-point free-energy correlation to two fundamental geometric quantities: the annealed probability that two independently sampled polymers, in the same environment, meet before reaching the prescribed terminal level, and the exit-point location of a single polymer. Our result is inspired in part by recent integration-by-parts work of Gu and Quastel for the KPZ equation. A crucial step in their continuous setting relies on an ingenious application of Itô's formula, which has no direct analogue in our semi-discrete setting. Instead, we exploit intrinsic symmetries of the polymer model together with the memoryless property. We also provide two applications: (i) we recover the horizontal Burke property by proving that the anchored stationary horizontal free-energy profile is a two-sided Brownian motion; (ii) in the zero-temperature limit, we obtain the corresponding identity for Brownian last-passage percolation.
ER -