Related papers: John Michael Hammersley (1920-2004)
This biographical and scientific memoir of Dominic Welsh includes summaries of his important contributions to probability and combinatorics. With John Hammersley, he introduced first-passage percolation, and in so doing they formulated and…
We describe some ideas of John Hammersley for proving the existence of critical exponents for two-dimensional self-avoiding walks and provide numerical evidence for their correctness.
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
The mathematical achievements of Harry Kesten since the mid-1950s have revolutionized probability theory as a subject in its own right and in its associations with aspects of algebra, analysis, geometry, and statistical physics. Through his…
Julian Besag was an outstanding statistical scientist, distinguished for his pioneering work on the statistical theory and analysis of spatial processes, especially conditional lattice systems. His work has been seminal in statistical…
In this paper we will prove a shape theorem for the last passage percolation model on a two dimensional $F$-compound Poisson process, called the Hammersley model with random weights. We will also provide diffusive upper bounds for shape…
This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade. Many more details can be found in hep-lat/9405016.
The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of…
The longest increasing subsequence problem for permutations has been studied extensively in the last fifty years. The interpretation of the longest increasing subsequence as the longest 21-avoiding subsequence in the context of permutation…
Wasssily Hoeffding's terminal illness and untimely death in 1991 put an end to efforts that were made to interview him for Statistical Science. An account of his scientific work is given in Fisher and Sen [The Collected Works of Wassily…
These lecture notes provide a rapid introduction to a number of rigorous results on self-avoiding walks, with emphasis on the critical behaviour. Following an introductory overview of the central problems, an account is given of the…
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…
Various lattice path models are reviewed. The enumeration is done using generating functions. A few bijective considerations are woven in as well. The kernel method is often used. Computer algebra was an essential tool. Some results are…
Prosopography is usually used to globally describe a large population of ordinary subjects. It is thus opposed to biography, as a genre devoted to exceptional individuals. I show in this article how to use prosopography to study a single…
Ever since J.M. Hammersley showed the existence of phase-transitions regarding independent bond percolation on general $d \geq 2$ dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most…
John Blake (1947--2016) was a leader in fluid mechanics, his two principal areas of expertise being biological fluid mechanics on microscopic scales and bubble dynamics. He produced leading research and mentored others in both Australia,…
Hammersley's Last-Passage Percolation (LPP), also known as Ulam's problem, is a well-studied model that can be described as follows: consider $m$ points chosen uniformly and independently in $[0,1]^2$, then what is the maximal number…
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…
This contribution to the book in honour of J.S. Bell will probably differ from the remaining ones, in particular since only a part of it will be devoted to specific technical arguments. In fact I have considered appropriate to share with…
There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the…