An Improved Upper Bound for the Right-Side Tail of the Crossover Distribution at the Edge of the Rarefaction Fan

TL;DR

This paper provides a tighter upper bound for the right-tail probability of a specific crossover distribution at the edge of a rarefaction fan, refining previous estimates in the context of stochastic processes.

Contribution

It introduces an improved upper bound for the right-side tail of the crossover distribution, enhancing understanding of its tail behavior at the rarefaction fan edge.

Findings

Established a sharper upper bound for the distribution's tail

Refined previous tail probability estimates

Contributes to the theoretical understanding of crossover distributions

Abstract

This note gives a proof of an improved upper bound for the right-side tail of a distribution discussed in "Crossover Distributions at the Edge of the Rarefaction Fan" by Ivan Corwin and Jeremy Quastel.