Recent progress in coalescent theory

N Berestycki - arxiv preprint arxiv:0909.3985, 2009‏ - arxiv.org
Coalescent theory is the study of random processes where particles may join each other to
form clusters as time evolves. These notes provide an introduction to some aspects of the …

[ספר][B] Spatial branching processes, random snakes and partial differential equations

JF Le Gall - 1999‏ - books.google.com
In these lectures, we give an account of certain recent developments of the theory of spatial
branching processes. These developments lead to several fas cinating probabilistic objects …

[ספר][B] Measure-Valued Branching Processes

Z Li, Z Li - 2011‏ - Springer
A measure-valued process describes the evolution of a population that evolves according to
the law of chance. In this chapter we provide some basic characterizations and constructions …

[ספר][B] The Lace Expansion and Its Applications: Ecole D'Eté de Probabilités de Saint-Flour XXXIV-2004

G Slade - 2006‏ - Springer
We consider independent Bernoulli bond percolation on the integer lattice Zd, with edge
(bond) set consisting of pairs {x, y} of vertices of Zd with y− x∈ Ω, where Ω defines either the …

Measures of success in a class of evolutionary models with fixed population size and structure

B Allen, CE Tarnita - Journal of mathematical biology, 2014‏ - Springer
We investigate a class of evolutionary models, encompassing many established models of
well-mixed and spatially structured populations. Models in this class have fixed population …

Modelling evolution in a spatial continuum

NH Barton, AM Etheridge, A Véber - Journal of Statistical …, 2013‏ - iopscience.iop.org
We survey a class of models for spatially structured populations which we have called
spatial Λ-Fleming–Viot processes. They arise from a flexible framework for modelling in …

[ספר][B] Voter model perturbations and reaction diffusion equations

JT Cox, R Durrett, EA Perkins - 2013‏ - numdam.org
We consider particle systems that are perturbations of the voter model and show that when
space and time are rescaled the system converges to a solution of a reaction diffusion …

[PDF][PDF] Convergence of critical oriented percolation to super-brownian motion above dimensions

R Van der Hofstad, G Slade - Annales de l'IHP Probabilités et …, 2003‏ - numdam.org
Van der Hofstad, Remco; Slade, Gordon. Convergence of critical oriented percolation to
super-brownian motion above $4+ 1$ dimensions. Annales de l'IHP Probabilités et …

Introductory lectures on stochastic population systems

DA Dawson - arxiv preprint arxiv:1705.03781, 2017‏ - arxiv.org
These notes provide a review of basic stochastic population models including branching
processes and models of population genetics. Measure-valued population models including …

Spatial Moran models, II: cancer initiation in spatially structured tissue

R Durrett, J Foo, K Leder - Journal of mathematical biology, 2016‏ - Springer
We study the accumulation and spread of advantageous mutations in a spatial stochastic
model of cancer initiation on a lattice. The parameters of this general model can be tuned to …