Contact process on regular tree with random vertex weights  

作　　者：Yu PAN Dayue CHEN Xiaofeng XUE 

机构地区：[1]LMAM, Peking University, Beijing 100871, China [2]School of Science, Beijing Jiaotong University Beijing 100044, China

出　　处：《Frontiers of Mathematics in China》2017年第5期1163-1181,共19页中国高等学校学术文摘·数学（英文）

摘　　要：This paper is concerned with the contact process with random vertex weights on regular trees, and studies the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection propagates through the edge connecting vertices x and y at rate λp（x）p（y） for someλ 〉0, where {ρ（x）, x∈ Td} are independent and identically distributed （i.i.d.） vertex weights. We show that when d is large enough, there is a phase transition at At（d）∈ （0, ec） such that for λ 〈 λc（d）, the contact process dies out, and for λ 〉 λc（d）, the contact process survives with a positive probability. Moreover, we also show that there is another phase transition at λe（d） such that for λ 〈 λe（d）, the contact process dies out at an exponential rate. Finally, we show that these two critical values have the same asymptotic behavior as d increases.This paper is concerned with the contact process with random vertex weights on regular trees, and studies the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection propagates through the edge connecting vertices x and y at rate λp（x）p（y） for someλ 〉0, where {ρ（x）, x∈ Td} are independent and identically distributed （i.i.d.） vertex weights. We show that when d is large enough, there is a phase transition at At（d）∈ （0, ec） such that for λ 〈 λc（d）, the contact process dies out, and for λ 〉 λc（d）, the contact process survives with a positive probability. Moreover, we also show that there is another phase transition at λe（d） such that for λ 〈 λe（d）, the contact process dies out at an exponential rate. Finally, we show that these two critical values have the same asymptotic behavior as d increases.

关 键 词：Contact process random vertex weights critical value ASYMPTOTICBEHAVIOR 

分 类 号：O211.6[理学—概率论与数理统计] O157.5[理学—数学]