相关论文: John Michael Hammersley (1920-2004)

This is about the mathematics and life of Donald Gordon Higman, 1928-2006. He did important work in representation theory of groups and algebras and in algebraic combinatorics. Charles C. Sims and Donald Higman discovered and constructed…

This is a concise mathematical introduction to Monte Carlo methods, a rich family of algorithms with far-reaching applications in science and engineering. Monte Carlo methods are an exciting subject for mathematical statisticians and…

In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability…

I published an interview of Leo Breiman in Statistical Science [Olshen (2001)], and also the solution to a problem concerning almost sure convergence of binary tree-structured estimators in regression [Olshen (2007)]. The former summarized…

We show that, for a stationary version of Hammersley's process, with Poisson ``sources'' on the positive x-axis, and Poisson ``sinks'' on the positive y-axis, an isolated second-class particle, located at the origin at time zero, moves…

We use the global stochastic analysis tools introduced by P. A. Meyer and L. Schwartz to write down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for exact symplectic manifolds, are characterized by a…

John Mather is a great scholar who was dedicated to mathematics in his whole life. His works in mathematics can be characterized as original and foundational. He laid out the foundation of singularity theory while he was a graduate student.…

This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties…

This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…

This is a brief survey of certain constants associated with random lattice models, including self-avoiding walks, polyominoes, the Lenz-Ising model, monomers and dimers, ice models, hard squares and hexagons, and percolation models.

Inferring how an epidemic will progress and what actions to take when presented with limited information is of critical importance for epidemiologists and health professionals. In real world settings, epidemiology data can be scarce or…

We describe the development of the mathematics of Helmut R. Salzmann (3. 11. 1930 -- 8. 3. 2022) and the main difficulties he was facing, documenting his lifelong productivity and his far reaching influence. We include a comprehensive…

The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…

The present paper gives an account for the general mathematical reader of the life and work of Martin Davis. Since two rather comprehensive autobiographical accounts and two long biographical interviews already exist, the present work…

Gerhard Hochschild's contribution to the development of mathematics in the XX century is succinctly surveyed. We start with a personal and mathematical biography, and then consider with certain detail his contributions to algebraic groups…

Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the early development of both fields. This paper is a bird's eye…

This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…

The effect of rotational constraint on the properties of lattice models like the self-avoiding walk, lattice animals and percolation is discussed. The results obtained so far, using a variety of exact and approximate techniques, are…

We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly…

This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…