149 citations · 560 across the 62 of their papers we have counts for
61 papers · 1 filter
Symmetrization for finitely dependent colouring
Alexander E. Holroyd
We prove the existence of a finitely dependent proper colouring of the integer lattice Z^d that is fully isometry-invariant in law, for all dimensions d. Previously this was known…
Cyclic products and optimal traps in cyclic birth and death chains
Mark Holmes, Alexander E. Holroyd, Alejandro Ramírez
A birth-death chain is a discrete-time Markov chain on the integers whose transition probabilities are non-zero if and only if . We consider birth-death chains w…
Minimal matchings of point processes
Alexander E. Holroyd, Svante Janson, Johan Wästlund
Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in . For a positive (respectively, negative) parameter we consider red-b…
The Life and Mathematical Legacy of Thomas M. Liggett
David Aldous, Pietro Caputo, Rick Durrett +3
Thomas Milton Liggett was a world renowned UCLA probabilist, famous for his monograph Interacting Particle Systems. He passed away peacefully on May 12, 2020. This is a perspective…
Galton-Watson games
Alexander E. Holroyd, James B. Martin
We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution i…
Perfect shuffling by lazy swaps
Omer Angel, Alexander E Holroyd
We characterize the minimum-length sequences of independent lazy simple transpositions whose composition is a uniformly random permutation. For every reduced word of the reverse pe…