Lamplighter graphs do not admit harmonic functions of finite energy
نویسندگان
چکیده
منابع مشابه
Lamplighter Graphs Do Not Admit Harmonic Functions of Finite Energy
We prove that a lamplighter graph of a locally finite graph over a finite graph does not admit a non-constant harmonic function of finite Dirichlet energy.
متن کاملHarmonic analysis of finite lamplighter random walks
Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path Z. In the present paper, we develop a spectral analysis for lamplighter random walks on finite graphs. In the general case, we use the C2-symmetry to reduce the spectral computations to a series of eigenvalue problems on the underlying graph. In th...
متن کاملPositive Harmonic Functions for Semi-isotropic Random Walks on Trees, Lamplighter Groups, and Dl-graphs
We determine all positive harmonic functions for a large class of “semiisotropic” random walks on the lamplighter group, i.e., the wreath product Zq ≀Z, where q ≥ 2. This is possible via the geometric realization of a Cayley graph of that group as the Diestel-Leader graph DL(q, q). More generally, DL(q, r) (q, r ≥ 2) is the horocyclic product of two homogeneous trees with respective degrees q+1...
متن کاملGroups Which Do Not Admit Ghosts
A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups C2 and C3. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups G the second p...
متن کاملRough Isometries and Dirichlet Finite Harmonic Functions on Graphs
Suppose that G\ and G% are roughly isometric connected graphs of bounded degree. If G\ has no nonconstant Dirichlet finite harmonic functions, then neither has Gi.
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: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10279-4