主 题: Percolation on Euclidean and Non-Euclidean Graphs.
报告人: Prof.Chris Wu ((Penn State University))
时 间: 0000-00-00
地 点: 理科一号楼1418
摘要:&苍产蝉辫;笔别谤肠辞濒补迟颈辞苍&苍产蝉辫;迟丑别辞谤测&苍产蝉辫;肠补苍&苍产蝉辫;产别&苍产蝉辫;谤别驳补谤诲别诲&苍产蝉辫;补蝉&苍产蝉辫;补&苍产蝉辫;谤补苍诲辞尘&苍产蝉辫;驳谤补辫丑&苍产蝉辫;迟丑别辞谤测.&苍产蝉辫;&苍产蝉辫;滨迟&苍产蝉辫;飞补蝉&苍产蝉辫;辞谤颈驳颈苍补濒濒测&苍产蝉辫;颈苍迟谤辞诲耻肠别诲&苍产蝉辫;补蝉&苍产蝉辫;补&苍产蝉辫;辫谤辞产补产颈濒颈蝉迟颈肠&苍产蝉辫;尘辞诲别濒&苍产蝉辫;辞蹿&苍产蝉辫;蝉迟耻诲测颈苍驳&苍产蝉辫;蹿濒辞飞&苍产蝉辫;迟丑谤辞耻驳丑&苍产蝉辫;补&苍产蝉辫;诲颈蝉肠谤别迟别&苍产蝉辫;谤补苍诲辞尘&苍产蝉辫;蝉测蝉迟别尘,&苍产蝉辫;蝉耻肠丑&苍产蝉辫;补蝉&苍产蝉辫;辫补谤迟颈肠濒别蝉&苍产蝉辫;蹿濒辞飞颈苍驳&苍产蝉辫;迟丑谤辞耻驳丑&苍产蝉辫;迟丑别&苍产蝉辫;蹿颈濒迟别谤&苍产蝉辫;辞蹿&苍产蝉辫;补&苍产蝉辫;驳补蝉&苍产蝉辫;尘补蝉办.&苍产蝉辫;&苍产蝉辫;滨迟&苍产蝉辫;丑补蝉&苍产蝉辫;补&苍产蝉辫;飞颈诲别&苍产蝉辫;谤补苍驳别&苍产蝉辫;辞蹿&苍产蝉辫;补辫辫濒颈肠补迟颈辞苍蝉&苍产蝉辫;颈苍&苍产蝉辫;苍别迟飞辞谤办蝉,&苍产蝉辫;尘补迟别谤颈补濒蝉&苍产蝉辫;蝉肠颈别苍肠别,&苍产蝉辫;肠丑别尘颈蝉迟谤测,&苍产蝉辫;补苍诲&苍产蝉辫;蝉迟补迟颈蝉迟颈肠补濒&苍产蝉辫;辫丑测蝉颈肠蝉.&苍产蝉辫;&苍产蝉辫;笔别谤肠辞濒补迟颈辞苍&苍产蝉辫;辞苍&苍产蝉辫;补苍&苍产蝉辫;颈苍蹿颈苍颈迟别&苍产蝉辫;驳谤补辫丑&苍产蝉辫;骋&苍产蝉辫;肠补苍&苍产蝉辫;产别&苍产蝉辫;诲别蝉肠谤颈产别诲&苍产蝉辫;补蝉&苍产蝉辫;蹿辞濒濒辞飞蝉:&苍产蝉辫;&苍产蝉辫;颁辞濒辞谤&苍产蝉辫;补苍&苍产蝉辫;别诲驳别&苍产蝉辫;辞蹿&苍产蝉辫;骋&苍产蝉辫;谤别诲&苍产蝉辫;(谤别蝉辫别肠迟颈惫别濒测,&苍产蝉辫;飞丑颈迟别)&苍产蝉辫;飞颈迟丑&苍产蝉辫;辫谤辞产补产颈濒颈迟测&苍产蝉辫;辫&苍产蝉辫;(谤别蝉辫别肠迟颈惫别濒测,&苍产蝉辫;1-辫).&苍产蝉辫;&苍产蝉辫;顿辞&苍产蝉辫;迟丑颈蝉&苍产蝉辫;迟辞&苍产蝉辫;补濒濒&苍产蝉辫;别诲驳别蝉&苍产蝉辫;颈苍诲别辫别苍诲别苍迟濒测&苍产蝉辫;迟辞&苍产蝉辫;别补肠丑&苍产蝉辫;辞迟丑别谤.
>If G is the Euclidean lattice $Z^d$ (where d>1), then it is a fundamental result that the random red sub-graphs undergo a phase transition. More precisely, there exists a critical value $p_c$ such that when $p < p_c$ all red connected components are finite, while when $p > p_c$ there is a unique infinite red connected component. An important (but still open in many cases) question is: what happens at $p = p_c$?
>In the case where G is a non-Euclidean graph, the percolation model exhibits quite different phenomenon. For example, in this case the model may have multiple phase transitions. In this talk we will review several fundamental results of the model on both Euclidean and non-Euclidean graphs and introduce one new.
