A geometric approach to on-diagonal heat kernel lower bounds on groups

By T. Coulhon, Alexander Grigorʼyan, C. Pittet. 2001

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/64643bcaa6d2ac82aadd75196cc0e027bfd77658

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. T. Coulhon
2. P. Auscher
3. Martin T. Barlow
4. Xuan Thinh Duong
5. Alexander Grigorʼyan
6. S. Hofmann
7. Prasad Tetali
8. Ravi Montenegro

In Geometry and Topology

1. Alexander Grigorʼyan
2. Martin T. Barlow
3. L. Saloff‐Coste
4. Prasad Tetali
5. Ravi Montenegro
6. T. Coulhon
7. Yuval Peres
8. C. Pittet

In Mathematical Physics

1. P. Auscher
2. T. Coulhon
3. S. Hofmann
4. Alexander Grigorʼyan
5. Martin T. Barlow
6. Xuan Thinh Duong
7. Prasad Tetali
8. Yuval Peres

Citations in the corpus

• Manifolds and graphs with slow heat kernel decay (2001, methodology): “So we prefer to give here a direct proof, using the method of anti-Faber-Krahn inequalities developed in [20] and [22], which is based in the following statement.”
• Riesz transform on manifolds and heat kernel regularity (2004, background): “In case 2, the doubling property is obvious, the heat kernel upper bound follows from [98] (but one has nowadays much simpler proofs, see for instance [ 21 ] for an exposition), and the gradient bound from [83].”
• Random walks on finite rank solvable groups (2003, methodology): “See also [ 6 ] and [18] for examples and special cases of the theorem.”
• ON RANDOM WALKS ON WREATH PRODUCTS (2002, background): “(iii) For a different proof of the case when K is finite, see [7].”
• Evolving sets, mixing and heat kernel bounds (2003, background): “For infinite Markov chains, Nash inequalities have been developed for general isoperimetric profiles; see Varopoulos [24], the survey by Pittet and Saloff Coste [21], the book [25], and especially the work of Coulhon [6, 7].”
• 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.”
• Mixing Time Bounds via the Spectral Profile (2005, methodology): “Lemma 3.1 gives a simple lower bound on the heat kernel. Lemma 3.1 ([ CGP01 ]).”