Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Yuan Zhang

Filter the Bibliography List

year	title	people

			clear

R. Durrett, T. Liggett, and Y. Zhang: “The contact process with fast voting,” Electron. J. Probab. 19 (2014), pp. Article no. 28, 19 pages. MR 3174840 Zbl 1291.60203 article

Consider a combination of the contact process and the voter model in which deaths occur at rate 1 per site, and across each edge between nearest neighbors births occur at rate \( \lambda \) and voting events occur at rate \( \theta \). We are interested in the asymptotics as \( \theta\to\infty \) of the critical value \( \lambda_c(\theta) \) for the existence of a nontrivial stationary distribution. In \( d\geq 3 \), \[ \lambda_c(\theta)\to 1/(2d\rho_d) \] where \( \rho_d \) is the probability a \( d \) dimensional simple random walk does not return to its starting point. In \( d = 2 \), \[ \lambda_c(\theta)/\log(\theta)\to 1/4\pi ,\] while in \( d=1 \), \( \lambda_c(\theta)/\theta^{1/2} \) has \[ \liminf \geq 1/\sqrt{2} \quad\text{and}\quad \limsup < \infty .\] The lower bound might be the right answer, but proving this, or even getting a reasonable upper bound, seems to be a difficult problem.

Yuan Zhang	Related
Richard Timothy Durrett	Related