172 citations · 1.1k across the 39 of their papers we have counts for
40 papers
The clumsy coupon collector's problem
Luke J. Attrill, Timothy M. Garoni
We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses al…
The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method
Timothy M. Garoni, Aram Perez, Zongzheng Zhou
We study the distribution of the magnetization of the critical mean-field O(N) model with N > 1. Specifically, we bound the Wasserstein distance between the finite-volume and limit…
Critical speeding-up in dynamical percolation
Eren Metin Elci, Timothy M. Garoni
We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in b…
Unwrapped two-point functions on high-dimensional tori
Youjin Deng, Timothy M. Garoni, Jens Grimm +1
We study unwrapped two-point functions for the Ising model, the self-avoiding walk and a random-length loop-erased random walk on high-dimensional lattices with periodic boundary c…
Two-point functions of random-length random walk on high-dimensional boxes
Youjin Deng, Timothy M. Garoni, Jens Grimm +1
We study the two-point functions of a general class of random-length random walks on finite boxes in $\ZZ^d$ with , and provide precise asymptotics for their behaviour. We s…
The length of self-avoiding walks on the complete graph
Youjin Deng, Timothy M Garoni, Jens Grimm +2
We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the numb…