Dylan J. Altschuler

works on

beck-fiala conjecture 1 discrepancy theory 1 metropolis walk 1 online algorithms 1 vector balancing 1

From the 1 of 10 linked papers with an AI index.

activity

20242026

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5 papers · 1 filter

math.MG2026

Metric PoincarÃ© 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 MatouÅ¡ek…

math.MG2025

Metric dimension reduction modulus for superlogarithmic distortion

Dylan J. Altschuler, Konstantin Tikhomirov

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

math.MG2025

Discrete Poincaré inequalities and universal approximators for random graphs

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

Nonlinear Poincaré inequalities are indispensable tools in the study of dimension reduction and low-distortion embeddings of graphs into metric spaces, and have found remarkable al…

math.MG2025

A combinatorial approach to nonlinear spectral gaps

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

A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular graph which satisfies the classical discrete PoincarÃ© inequality for scalar functions, also sa…

math.MG2025

Universal geometric non-embedding of random regular graphs

Dylan J. Altschuler, Konstantin Tikhomirov

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