These notes provide a review of basic stochastic population models including branching
processes and models of population genetics. Measure-valued population models including …

We review several connections between percolation and SEIR epidemic models. In the first
part we analyze the role of percolation in representing or approximating an epidemic model; …

In this paper we introduce a contact process on a dynamical long range percolation
(CPDLP) defined on a complete graph (V, E). A dynamical long range percolation is a Feller …

We study long-range percolation on the hierarchical lattice of order N, where any edge of
length k is present with probability p_k=1-\exp(-β^-kα), independently of all other edges. For …

We study the percolation in the hierarchical lattice of order N where the probability of
connection between two nodes separated by a distance k is of the form min {αβ-k, 1}, α≥ 0 …

We perform various changes of measure in the lookdown particle system of Donnelly and
Kurtz. The first example is a product type h-transform related to conditioning a Generalized …

= P [X0= x0] P (x0, x1)··· P (xn− 1, xn), where in the last step we have used the induction
hypothesis. To check that conversely (1. 2) implies (1.1), by the definition of the conditional …

What is the long-time behavior of the law of a contact process started with a single infected
site, distributed according to counting measure on the lattice? This question is related to the …

This paper gives a new, simple proof of the known fact that for contact processes on general
lattices, in the subcritical regime the expected number of infected sites decays exponentially …

We study transience and recurrence of simple random walks on percolation clusters in the
hierarchical group of order N, which is an ultrametric space. The connection probability on …