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Pooya Vahidi Ferdowsi

Publications and source records attributed to Pooya Vahidi Ferdowsi.

5 recordsLinked to original sources
arXiv2019

Quasi-Regular Sequences

Let $Σ$ be a countable alphabet. For $r\geq 1$, an infinite sequence $s$ with characters from $Σ$ is called $r$-quasi-regular, if for each $σ\inΣ$ the ratio of the longest to shortest interval between consecutive occurrences of $σ$ in $s$ is bounded by $r$. In this paper, we answer a question asked by Kempe, Schulman, and Tamuz, and prove that for any probability distribution $\mathbf{p}$ on a finite alphabet $Σ$, there exists a $2$-quasi-regular infinite sequence with characters from $Σ$ and density of characters equal to $\mathbf{p}$. We also prove that as $\left\lVert\mathbf{p}\right\rVert_\infty$ tends to zero, the infimum of $r$ for which $r$-quasi-regular sequences with density $\mathbf{p}$ exist, tends to one. This result has a corollary in the Pinwheel Problem: as the smallest integer in the vector tends to infinity, the density threshold for Pinwheel schedulability tends to one.

math.CO↗
arXiv2019

Strong amenability and the infinite conjugacy class property

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.

math.GR↗
arXiv2019

Choquet-Deny groups and the infinite conjugacy class property

A countable discrete group $G$ is called Choquet-Deny if for every non-degenerate probability measure $μ$ on $G$ it holds that all bounded $μ$-harmonic functions are constant. We show that a finitely generated group $G$ is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that $G$ is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when $G$ is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.

math.GR↗
arXiv2018

Non-virtually nilpotent groups have infinite conjugacy class quotients

We offer in this note a self-contained proof of the fact that a finitely generated group is not virtually nilpotent if and only if it has a quotient with the infinite conjugacy class (ICC) propoerty. This proof is a modern presentation of the original proof, by McLain (1956) and Duguid and McLain (1956).

math.GR↗