Spectral Computations on Lamplighter Groups and Diestel-Leader Graphs
نویسندگان
چکیده
منابع مشابه
Spectral Computations on Lamplighter Groups and Diestel-leader Graphs
The Diestel-Leader graph DL(q, r) is the horocyclic product of the homogeneous trees with respective degrees q+1 and r+1. When q = r, it is the Cayley graph of the lamplighter group (wreath product) Zq≀Z with respect to a natural generating set. For the “Simple random walk” (SRW) operator on the latter group, Grigorchuk and Żuk and Dicks and Schick have determined the spectrum and the (on-diago...
متن کاملGreen kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs
We determine the precise asymptotic behaviour (in space) of the Green kernel of simple random walk with drift on the Diestel–Leader graph DL(q, r), where q, r 2. The latter is the horocyclic product of two homogeneous trees with respective degrees q + 1 and r + 1. When q = r , it is the Cayley graph of the wreath product (lamplighter group) Zq Z with respect to a natural set of generators. We d...
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We investigate various features of a quite new family of graphs, introduced as a possible example of vertex-transitive graph not roughly isometric with a Cayley graph of some finitely generated group. We exhibit a natural compactification and study a large class of random walks, proving theorems concerning almost sure convergence to the boundary, a strong law of large numbers and a central limi...
متن کاملLamplighters, Diestel-Leader Graphs, Random Walks, and Harmonic Functions
The lamplighter group over Z is the wreath product Zq ≀ Z. With respect to a natural generating set, its Cayley graph is the Diestel-Leader graph DL(q, q). We study harmonic functions for the “simple” Laplacian on this graph, and more generally, for a class of random walks on DL(q, r), where q, r ≥ 2. The DL-graphs are horocyclic products of two trees, and we give a full description of all posi...
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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...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2005
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-005-3079-0