Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems.
Some non-markovian Osterwalder-Schrader fields
Some properties of annulus SLE.
Some results for poisoning in a catalytic model.
Some two-dimensional finite energy percolation processes.
Some use of some “symmetries” of some random process
Spatial birth-and-dead processes in random environment.
Special points of the Brownian net.
Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems
Spectral gap for an unrestricted Kawasaki type dynamics
Spectral gap for an unrestricted Kawasaki type dynamics
We give an accurate asymptotic estimate for the gap of the generator of a particular interacting particle system. The model we consider may be informally described as follows. A certain number of charged particles moves on the segment [1,L] according to a Markovian law. One unitary charge, positive or negative, jumps from a site k to another site k'=k+1 or k'=k-1 at a rate which depends on the charge at site k and at site k'. The total charge of the system is preserved by the dynamics, in...
Spectral gap for the interchange process in a box.
Spontaneous breaking of continuous rotational symmetry in two dimensions.
Standard stochastic coalescence with sum kernels.
State classification for a class of interacting superprocesses with location dependent branching.
State dependent multitype spatial branching processes and their longtime behavior.
Stationary measures and phase transition for a class of probabilistic cellular automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Stationary measures and phase transition for a class of Probabilistic Cellular Automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Statistical study of Navier-Stokes equations, I
Steady state and scaling limit for a traffic congestion model
In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...