Publications [#243539] of Richard T. Durrett

Papers Published

1. Durrett, R; Remenik, D, Chaos in a spatial epidemic model, Annals of Applied Probability, vol. 19 no. 4 (August, 2009), pp. 1656-1685, Institute of Mathematical Statistics, ISSN 1050-5164 [MR2010k:60322], [doi]
   (last updated on 2024/04/24)

   Abstract:
   We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the d-dimensional lattice and torus, with d = 2. On the finite graphs with global dispersal or with a dispersal radius that grows with the number of sites, we prove convergence to a dynamical system that is chaotic for some parameter values. We conjecture that on the infinite lattice with a fixed finite dispersal distance, distant parts of the lattice oscillate out of phase so there is a unique nontrivial stationary distribution. © Institute of Mathematical Statistics, 2009.