Spectral Analysis on Homogeneous Trees
نویسندگان
چکیده
منابع مشابه
Anisotropic Contact Process on Homogeneous Trees
The existence of a weak survival region is established for the anisotropic symmetric contact process on a homogeneous tree T2d of degree 2d ≥ 4 : For parameter values in a certain connected region of positive Lebesgue measure, the population survives forever with positive probability but ultimately vacates every finite subset of the tree with probability one. In this phase, infection trails mus...
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Sufficient conditions for the existence of a weak survival phase are given for an anisotropic contact process on a homogeneous tree. These require that the contact process be homogeneous, that is, for any two vertices x, y of the tree there is an automorphism mapping x to y leaving the infection rates invariant; and that the contact process be weakly symmetric, that is, for each vertex there sh...
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Abstract. In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol classes and associated operators. We prove that these operators are bounded on L and give adjoint and product formulas. Finally we compute the symb...
متن کاملBiharmonic Green Functions on Homogeneous Trees
The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk D in C arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of t...
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Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset 3 of the boundary consisti...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1998
ISSN: 0196-8858
DOI: 10.1006/aama.1997.0570