Time Correlation Exponents in Last Passage Percolation

Riddhipratim Basu; Shirshendu Ganguly

Paper

Time Correlation Exponents in Last Passage Percolation

Abstract

For directed last passage percolation on

with exponential passage times on the vertices, let

denote the last passage time from

. We consider asymptotic two point correlation functions of the sequence

. In particular we consider

for

where

with

. We show that in the former case

whereas in the latter case

. 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

process coming from exponential LPP, and precise variance estimates for lengths of polymers constrained to be inside thin rectangles at the transversal fluctuation scale.