5 citations · 9 across the 7 of their papers we have counts for
9 papers
The invariant random order extension property is equivalent to amenability
Andrei Alpeev
Recently, Glasner, Lin and Meyerovitch gave a first example of a partial invariant order on a certain group that cannot be invariantly extended to an invariant random total order.…
Examples of measures with trivial left and non-trivial right random walk tail boundary
Andrei Alpeev
In early 80's Vadim Kaimanovich presented a construction of a non-degenerate measure, on the standard lamplighter group, that has a trivial left and non-trivial right random walk t…
Lamplighters over non-amenable groups are not strongly Ulam stable
Andrei Alpeev
We prove that a wreath product of an abelian group and a non-amenable group is not strongly Ulam stable. Previously this was known for groups containing free subgroups, due to work…
Entropy inequalities and exponential decay of correlations for unique Gibbs measures on trees
Andrei Alpeev
In a recent paper by A. Backhausz, B. Gerencsér and V. Harangi, it was shown that factors of independent identically distributed random processes (IID) on trees obey certain geomet…
Predictability, topological entropy and invariant random orders
Andrei Alpeev, Tom Meyerovitch, Sieye Ryu
We prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman. On route, we investigate invariant random or…
Kolmogorov complexity and entropy of amenable group actions
Andrei Alpeev
It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable gro…