We give algebraic characterizations for expansiveness of algebraic actions of countable
groups. The notion of p p-expansiveness is introduced for algebraic actions, and we show …

Combinatorial Independence and Sofic Entropy | Communications in Mathematics and
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This survey is an extended version of lectures given at the Cornell Probability Summer
School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and …

We compute the eigenvalues of up-Laplacians on cubical lattices and derive the torsion-
weighted count of spanning acycles in cubical lattices by using the matrix-tree theorem for …

Homoclinic points, atoral polynomials, and periodic points of algebraic Zd-actions Page 1
Ergod. Th. & Dynam. Sys. (2013), 33, 1060–1081 c Cambridge University Press, 2012 doi:10.1017/S014338571200017X …

We give a non-trivial upper bound for the critical density when stabilizing iid distributed
sandpiles on the lattice Z^ 2 Z 2. We also determine the asymptotic spectral gap, asymptotic …

We prove a number of identities relating the sofic entropy of a certain class of non-expansive
algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree …

We use ideas from quantitative homogenization to show that nonconstant harmonic
functions on the percolation cluster cannot satisfy certain structural constraints, for example …

This survey is an extended version of lectures given at the Cornell Probability Summer
School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and …

We prove that the Galois equidistribution of torsion points of the algebraic torus $\mathbb {G}
_ {m}^ d $ extends to the singular test functions of the form $\log {| P|} $, where $ P $ is a …