Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 154 tok/s
Gemini 2.5 Pro 44 tok/s Pro
GPT-5 Medium 33 tok/s Pro
GPT-5 High 27 tok/s Pro
GPT-4o 110 tok/s Pro
Kimi K2 191 tok/s Pro
GPT OSS 120B 450 tok/s Pro
Claude Sonnet 4.5 38 tok/s Pro
2000 character limit reached

Time Correlation Exponents in Last Passage Percolation (1807.09260v2)

Published 24 Jul 2018 in math.PR, math-ph, and math.MP

Abstract: For directed last passage percolation on $\mathbb{Z}2$ with exponential passage times on the vertices, let $T_{n}$ denote the last passage time from $(0,0)$ to $(n,n)$. We consider asymptotic two point correlation functions of the sequence $T_{n}$. In particular we consider ${\rm Corr}(T_{n}, T_{r})$ for $r\le n$ where $r,n\to \infty$ with $r\ll n$ or $n-r \ll n$. We show that in the former case ${\rm Corr}(T_{n}, T_{r})=\Theta((\frac{r}{n}){1/3})$ whereas in the latter case $1-{\rm Corr}(T_{n}, T_{r})=\Theta ((\frac{n-r}{n}){2/3})$. The argument revolves around finer understanding of polymer geometry and is expected to go through for a larger class of integrable models of last passage percolation. As by-products of the proof, we also get a couple of other results of independent interest: Quantitative estimates for locally Brownian nature of pre-limits of Airy$_2$ process coming from exponential LPP, and precise variance estimates for lengths of polymers constrained to be inside thin rectangles at the transversal fluctuation scale.

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Open Questions

We haven't generated a list of open questions mentioned in this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.