The scaling limit of senile reinforced random walk.
The scaling limits of a heavy tailed Markov renewal process
In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the -stable regenerative set. We then apply these results to the strip wetting model which is a random walk constrained above a wall and rewarded or penalized when it hits the strip where is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.
The shape of a typical boxed plane partition.
The single server queue and the storage model: large deviations and fixed points.
The single server queue with Erlang input and semi-Markov service times
The size of a pond in 2D invasion percolation.
The spatial -coalescent.
The spectral gap for a Glauber-type dynamics in a continuous gas
The spread of a catalytic branching random walk
We consider a catalytic branching random walk on that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position : For some constant , almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for as goes to infinity.
The stationary G/G/ queue.
The stationary G/G/ queue with non-identical servers.
The stationary local sojourn time in single server tandem queues with renewal input.
The stationary waiting time and other variables in single-server queues with specialities at the beginning of a busy period
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial
The superposition of two independent Markov renewal processes
The survival probability for critical spread-out oriented percolation above dimensions. II. Expansion
The theory of networks of single server queues and the tandem queue model.
The time constant and critical probabilities in percolation models.
The time constant vanishes only on the percolation cone in directed first passage percolation.
The time for a critical nearest particle system to reach equilibrium starting with a large gap.