J. A. Fill

collaborators

5 papers

math.PR2026

Positive autocorrelation at unit lag for stationary random walk Metropolis-Hastings in $R^{d}$

James Allen Fill, Svante Janson

It is often asserted in the literature that one should expect positive autocorrelation for random walk Metropolis-Hastings (RWMH), especially if the typical proposal step-size is s…

math.PR2026

A new fine-scale Berry-Esseen-type Gumbel-limit theorem for multivariate maxima

James Allen Fill

For $d \geq 2$ and i.i.d. $d$ -dimensional observations $X^{(1)}, X^{(2)}, \dots$ with independent Exponential $(1)$ coordinates, let $I ¨ _{n}$ denote the minimum $\e…

math.PR2025

An interesting spectral gap problem, from Jim Fill

James Allen Fill

At the request of Laszlo Babai, founder and an editor of the free online journal Theory of Computing (ToC), theoryofcomputing.org, in August, 2025, I am posting on the arXiv, essen…

math.PR2025

Disintegration theorem for multifunctions, with applications to empirical Wasserstein distances and average-case statistical bounds

James Allen Fill, Lachlan Ewen MacDonald

We prove a generalisation of the disintegration theorem to the setting of multifunctions between Polish probability spaces. Whereas the classical disintegration theorem guarantees…

math.PR2025

Convergence of the QuickVal Residual

James Allen Fill, Jason Matterer

QuickSelect (aka Find), introduced by Hoare (1961), is a randomized algorithm for selecting a specified order statistic from an input sequence of $n$ objects, or rather their ident…

Positive autocorrelation at unit lag for stationary random walk Metropolis-Hastings in Rd

A new fine-scale Berry-Esseen-type Gumbel-limit theorem for multivariate maxima

An interesting spectral gap problem, from Jim Fill

Disintegration theorem for multifunctions, with applications to empirical Wasserstein distances and average-case statistical bounds

Convergence of the QuickVal Residual

Positive autocorrelation at unit lag for stationary random walk Metropolis-Hastings in $R^{d}$