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We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow…
We study the phase structure of a surface model by using the canonical Monte Carlo simulation technique on triangulated, fixed connectivity, and spherical surfaces with many fine holes. The size of a hole is assumed to be of the order of…
When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system in which P much greater than L, our natural intuition tells us that the box with the average number of balls has the…
Theory of granular dissipative gas is discussed based on Boltzmann's equation and in view of recent experimental results in micro-gravity during few CNES and ESA campaigns [9,11]. It is recalled that the Boltzmann's distribution is a steady…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous time simple random walk on the d-dimensional lattice. These particles are called A-particles and move independently…
A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
In this paper we consider the existence of Hamilton cycles and perfect matchings in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…
We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a…
We consider a variation of balls-into-bins which randomly allocates $m$ balls into $n$ bins. Following Godfrey's model (SODA, 2008), we assume that each ball $t$, $1\le t\le m$, comes with a hypergraph…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given $\alpha \in (0,1)$, the union of any $n$-vertex graph with minimum degree $\alpha n$ and the binomial random…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
We study a dynamical system motivated by our earlier work on the statistical physics of social balance on graphs that can be viewed as a generalization of annihilating walks along two directions: first, the interaction topology is a…
We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the…