6 papers · 1 filter
Positive autocorrelation at unit lag for stationary random walk Metropolis-Hastings in
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…
A new fine-scale Berry-Esseen-type Gumbel-limit theorem for multivariate maxima
James Allen Fill
For and i.i.d. -dimensional observations with independent Exponential coordinates, let denote the minimum $\e…
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…
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…
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 objects, or rather their ident…
On the probability of a Pareto record
James Allen Fill, Ao Sun
Given a sequence of independent random vectors taking values in and having common continuous distribution function , say that the observ…