A note about Domination and monotonicity in disordered systems

TL;DR

This paper explores inequalities and monotonicity properties of free energy in directed polymers and related disordered systems using stochastic orders, providing new insights into their probabilistic behavior.

Contribution

It introduces new inequalities and monotonicity results for free energy in disordered systems under various stochastic orders, extending classical results.

Findings

Established inequalities for free energy

Proved monotonicity properties under stochastic orders

Extended results to classical disordered systems

Abstract

In this note we establish several inequalities and monotonicity properties for the free energy of directed polymers under certain stochastic orders: the usual stochastic order, the Laplace transform order and the convex order. For the latter our results cover also many classical disordered systems.