Konstantin E. Tikhomirov

collaborators

4 papers

math.PR2025

A threshold for online balancing of sparse i.i.d. vectors

Dylan J. Altschuler, Konstantin Tikhomirov

Consider the task of \textit{online} vector balancing for stochastic arrivals $(X_{i})_{i \in [T]}$ , where the time horizon satisfies $T = Θ (n)$ , and the $X_{i}$ are i.i.d uniform $d$ -…

math.MG2025

Metric Poincaré inequalities for graphs

Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1

This article obtains purely metric counterparts of cornerstone results in the theory of embedding graphs into normed spaces. Our first main result is a metric analogue of Matoušek'…

math.MG2025

Metric dimension reduction modulus for superlogarithmic distortion

Dylan J. Altschuler, Konstantin Tikhomirov

The metric dimension reduction modulus $k_{n}^{α} (ℓ_{\infty})$ is the smallest $k$ such that every $n$ --point metric space can be embedded into some $k$ -dimensional normed space, with…

math.MG2025

Universal geometric non-embedding of random regular graphs

Dylan J. Altschuler, Konstantin Tikhomirov

Let $Δ \geq 3$ be fixed, $n \geq n_{Δ}$ be a large integer. It is a classical result that $Δ$ --regular expanders on $n$ vertices are not embeddable as geometric (distance) graphs into E…