Cram\'er transform and t-entropy

TL;DR

This paper explores the relationship between t-entropy and the Cramér transform in the context of weighted composition operators, revealing how the spectral radius relates to these concepts and providing explicit expressions.

Contribution

It establishes a novel connection between t-entropy and the Cramér transform of the spectral radius of weighted composition operators, extending understanding in spectral theory and entropy.

Findings

Expresses the Cramér transform of the spectral radius via t-entropy

Provides explicit formulas linking spectral radius and t-entropy

Enhances theoretical understanding of weighted composition operators

Abstract

t-entropy is the convex conjugate of the logarithm of the spectral radius of a weighted composition operator (WCO). Let $X$ be a nonnegative random variable. We show how the Cram\'er transform with respect to the spectral radius of WCO is expressed by the t-entropy and the Cram\'er transform of the given random variable X.