Rate of convergence of stochastic processes with values in $\mathbb{R}$-trees and Hadamard manifolds

TL;DR

This paper establishes a Gaussian upper bound for tail probabilities of mean values of i.i.d. random variables taking values in $\

Contribution

It extends tail probability bounds to stochastic processes valued in $\\mathbb{R}$-trees and Hadamard manifolds under Sturm's framework.

Findings

Gaussian upper bound for tail probabilities

Applicable to $\\mathbb{R}$-trees and Hadamard manifolds

Generalizes previous bounds to new geometric contexts

Abstract

Under K.-T. Sturm's formulation, we obtain a Gaussian upper bound for tail probability of mean value of independent, identically distributed random variables with values in $\mathbb{R}$-trees and Hadamard manifolds.