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The contact process with fast voting


 
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1. Title Title of document The contact process with fast voting
 
2. Creator Author's name, affiliation, country Rick Durrett; Duke; United States
 
2. Creator Author's name, affiliation, country Thomas Liggett; UCLA
 
2. Creator Author's name, affiliation, country Yuan Zhang; Duke
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) contact process, voter model, block construction
 
3. Subject Subject classification 60K35
 
4. Description Abstract 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 $d \ge 3$, $\lambda_c(\theta) \to 1/(2d\rho_d)$ 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 $\liminf \ge 1/\sqrt{2}$ and $\limsup < \infty$.The lower bound might be the right answer, but proving this, or even getting a reasonable upper bound, seems to be a difficult problem.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2014-03-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3021
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3021
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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