Critical percolation of virtually free groups and other tree-like graphs
نویسندگان
چکیده
منابع مشابه
commuting and non -commuting graphs of finit groups
فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
15 صفحه اولCritical Percolation of Free Product of Groups
In this article we study percolation on the Cayley graph of a free product of groups. Such a graph has a tree-like structure which allows us to evaluate the critical values of the phase transition, mean cluster size and the critical exponent in bond percolation.
متن کاملFinite automata for Schreier graphs of virtually free groups
The Stallings construction for f.g. subgroups of free groups is generalized by introducing the concept of Stallings section, which allows an efficient computation of the core of a Schreier graph based on edge folding. It is proved that those groups admitting Stallings sections are precisely f.g. virtually free groups, through a constructive approach based on Basse-Serre theory. Complexity issue...
متن کاملCritical percolation on Cayley graphs of groups acting on trees
This article presents a method for finding the critical probability pc for the Bernoulli bond percolation on graphs with the so called tree-like structure. Such graphs can be decomposed into a tree of pieces which have finitely many isomorphism classes. This class of graphs includes the Cayley graphs of amalgamated products, HNN extensions or general groups acting on trees. It also includes all...
متن کاملA Characterisation of Virtually Free Groups
We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/09-aop458