On high dimensional directed polymer in random media
Matteo Marsili (Dept. of Theor. Physics, University of Manchester)
TL;DR
This paper investigates high-dimensional directed polymers in random media, demonstrating that their behavior can resemble independent variables under certain conditions, despite strong correlations.
Contribution
It introduces a method to analyze high-dimensional directed polymers by leveraging extreme statistics and pairwise correlation control.
Findings
Behavior similar to independent variables in high dimensions
Applicable to low energy directed polymer ensembles
Uses asymptotic extreme statistics theory
Abstract
Directed polymers in random media are studied using results of the asymptotic theory of extreme statistics. Despite the strong correlation, one can recover the behavior of independent random variables for high dimensions, using a result which requires only a control of pairwise correlation, and focussing on ensembles of low energy directed polymers.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods