Related papers: Size-biased diffusion limits and the inclusion pro…
The Gamma-Dirichlet structure corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process…
We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing diffusivity. Such diffusion processes arise…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with are the Aldous-Diaconis-Hammersley process and the related stick model. The A-D-H process represents a particle…
We propose a stochastic description of the dynamics of a Bose-Einstein condensate within the context of Nelson stochastic mechanics. We start from the $N$ interacting conservative diffusions, associated with the $N$ Bose particles, and take…
When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initial configuration $\xi=\sum_{j \in…
We consider a zero-range process $\eta^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12\Delta u^\alpha, \alpha>1$. As a main result we…
When water is present in a medium with pore sizes in a range around 10nm the corresponding freezing point depression will cause long range broadening of a melting front. Describing the freezing-point depression by the Gibbs-Thomson equation…
In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172--182] for sums of uniformly null…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
The inclusion process is a stochastic lattice gas, which is a natural bosonic counterpart of the well-studied exclusion process and has strong connections to models of heat conduction and applications in population genetics. Like the…
Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in [0,1]^\N: \sum_{i\ge 1} x_i=1\}$ with GEM…
The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…
We perform a two-dimensional molecular-dynamics study of a model for sheared bidisperse granular systems under conditions of simple shear and Poiseuille flow. We propose a mechanism for particle-size segregation based on the observation…
We study linear statistics of a class of determinantal processes which interpolate between Poisson and GUE/Ginibre statistics in dimension 1 or 2. These processes are obtained by performing an independent Bernoulli percolation on the…
We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and further studied in [Cor14], by allowing…