منابع مشابه
Random Walks on Ramanujan Complexes and Digraphs
The cutoff phenomenon was recently confirmed for random walks on Ramanujan graphs by the first author and Peres. In this work, we obtain analogs in higher dimensions, for random walk operators on any Ramanujan complex associated with a simple group G over a local field F . We show that if T is any k-regular G-equivariant operator on the Bruhat–Tits building with a simple combinatorial property ...
متن کاملRAMANUJAN COMPLEXES OF TYPE Ad*
We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of type Ad-1 associated with PGLd(F) where F is a local field of positive characteristic. 1. I n t r o d u c t i o n A finite k-regular graph X is called a Ramanujan graph if for every eigen...
متن کاملExplicit Constructions of Ramanujan Complexes
In [LSV] we defined and proved the existence of Ramanujan complexes, see also [B1], [CSZ] and [Li]. The goal of this paper is to present an explicit construction of such complexes. Our work is based on the lattice constructed by Cartwright and Steger [CS]. This remarkable discrete subgroup Γ of PGLd(F ), when F is a local field of positive characteristic, acts simply transitively on the vertice...
متن کاملSpectrum and Combinatorics of Ramanujan Triangle Complexes
Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high-dimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.
متن کاملThe Ramanujan Property for Regular Cubical Complexes
We consider cubical complexes which are uniformized by an ordered product of regular trees. For these we define the notion of being Ramanujan, generalizing the one-dimensional definition introduced by Lubotzky, Phillips, and Sarnak [15]. As in [12], we also allow local systems. We discuss the significance of this property, and then we construct explicit arithmetic examples using quaternion alge...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2009
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-09880-3