Improved Estimates of Survival Probabilities via Isospectral Transformations

TL;DR

This paper introduces a novel method using isospectral graph transformations to improve the estimation of survival probabilities in open dynamical systems derived from one-dimensional maps.

Contribution

It applies isospectral graph transformations to enhance survival probability estimates, outperforming traditional direct methods.

Findings

Improved accuracy of survival probability estimates

Demonstrated effectiveness on systems with finite Markov partitions

Showed superiority over existing direct estimation approaches

Abstract

We consider open systems generated from one-dimensional maps that admit a finite Markov partition and use the recently developed theory of isospectral graph transformations to estimate a system's survival probabilities. We show that these estimates are better than those obtained through a more direct approach.