Parabolic Harnack inequality and local limit theorem for percolation clusters.
Percolation beyond , many questions and a few answers.
Percolation of arbitrary words on the close-packed graph of .
Percolation on fuchsian groups
Percolation on nonamenable products at the uniqueness threshold
Percolation, Perimetry, Planarity.
Percolation times in two-dimensional models for excitable media.
Percolation transition for some excursion sets.
Perturbing the hexagonal circle packing: a percolation perspective
We consider the hexagonal circle packing with radius and perturb it by letting the circles move as independent Brownian motions for time . It is shown that, for large enough , if is the point process given by the center of the circles at time , then, as , the critical radius for circles centered at to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...
Phase coexistence in Ising, Potts and percolation models
Phase diagram of the Potts model in an external magnetic field
Phase transition and Martin boundary
Phase transition for the frog model.
Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation
We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and diffusion.
Poisson trees, succession lines and coalescing random walks
Positively and negatively excited random walks on integers, with branching processes.
Potential scattering in stochastic mechanics
Potential spaces on fractals
We introduce potential spaces on fractal metric spaces, investigate their embedding theorems, and derive various Besov spaces. Our starting point is that there exists a local, stochastically complete heat kernel satisfying a two-sided estimate on the fractal considered.
Prime percolation.
Probability estimates for symmetric simple exclusion random walks