Manifolds and graphs with slow heat kernel decay

By Martin T. Barlow, T. Coulhon, Alexander Grigorʼyan. 2001

153 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8970c962c418712bc91c818d06ae4794055942a9

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs (2005, background): “KUMAGAI bound hn C x 6 x D J cn G α e β , which follows from C LHK C β D;D , must be compatible with the upper bound hn C x 6 x D M C n G α e,r α ? 1 s from [12].”
Riesz transform and related inequalities on non‐compact Riemannian manifolds (2003, background): “Consider a discretization 0 of the manifold M (see [12, 20, 29]); here 0 can be identified with the Vicsek graph out of which M was built (see [6]).”
Harnack inequalities and sub-Gaussian estimates for random walks (2002, unknown): “Due to the tree structure of Γ , it is easy to compute the Green kernel g Γk (xk, ·) (cf. [ 7, Section 4 ]).”
Sub-Gaussian estimates of heat kernels on infinite graphs, to appera in Duke Math (2001, background): “By [ 9, Theorem 2.1 ], the lower bound in (V ) implies the ondiagonal upper bound pn(x, x) ≤ Cn−α/(α+1).”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “oretic sense, which motivates a large part of our work. Consideration of fractals in this context is important, in particular, because they appear as models for manifolds with slow heat kernel decay, [11], and limit sets of Schreier graphs of self-similar groups, which include groups of intermediate”
Mathematical Aspects of Mixing Times in Markov Chains (2006, methodology): “The functional analog of some of this is done via the spectral profile, developed for the present context of finite Markov chains, in [34], while having its origins in the developments by [4] and [18] in the context of manifolds.”