相关论文: Hastings-Levitov aggregation in the small-particle…

We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…

We prove that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence $(p_n)$ of even positive integers with $p_n\sim 2\alpha \sqrt{2n}$ for some $\alpha\in(0,\infty)$. Then, for the…

We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…

We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted…

The main topic of these lecture notes is the continuum scaling limit of planar lattice models. One reason why this topic occupies an important place in the theory of probability and mathematical statistical physics is that scaling limits…

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size $N$ onto stochastic networks, computing transition probabilities…

The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the…

We establish the exponential clustering of correlation functions for the high-temperature Gibbs states of Bose-Hubbard type models. To overcome the technical difficulties arising from the unboundedness of bosonic operators, we develop the…

We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…

We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy and the…

We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…

In this paper, we are concerned with the large N limit of linear combinations of the entries of a Brownian motion on the group of N by N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one.…

We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…

The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…

The evolution of a planar perturbation in a Einstein-de Sitter Universe is studied using a previously introduced Lagrangian scheme. An approximate discrete dynamical system is derived, which describes the mass agglomeration process…

We study the structure of extreme level sets of a standard one dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such…

We study the scaling limits of looptrees associated with Bienaym\'e--Galton--Watson (BGW) trees, that are obtained by replacing every vertex of the tree by a "cycle" whose size is its degree. First, we consider BGW trees whose offspring…

We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also…

We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…