On Groups, Slow Heat Kernel Decay Yields Liouville Property and Sharp Entropy Bounds

Author:

Peres Yuval1,Zheng Tianyi2

Affiliation:

1. One Microsoft Way, Redmond, WA

2. Department of Mathematics, University of California San Diego, La Jolla, CA

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference32 articles.

1. A lower estimate for central probabilities on polycyclic groups;Alexopoulos;Canad. J. Math.,1992

2. Speed exponents of random walks on groups;Amir;Int. Mathematics Res. Notices,2012

3. Groups with minimal harmonic functions as small as you like.;Amir,2016

4. The wreath product of $\mathbb{Z}$ with $\mathbb{Z}$ has Hilbert compression exponent $\frac{2}{3}$;Austin;Proc. Amer. Math. Soc.,2009

5. Avez, A. “Harmonic functions on groups.” In Differential Geometry and Relativity, 27–32. Mathematical Phys. and Appl. Math., vol. 3, 1976.Dordrecht: Reidel.

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1. Collisions of random walks in dynamic random environments;Electronic Journal of Probability;2022-01-01

2. Law of large numbers for the drift of the two-dimensional wreath product;Probability Theory and Related Fields;2021-12-06

3. No Percolation at Criticality on Certain Groups of Intermediate Growth;International Mathematics Research Notices;2019-12-06

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