Clayton Mizgerd

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20212026

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math.CO2026

Equality in Fill's spectral gap problem

Vishesh Jain, Clayton Mizgerd

We study the adjacent-transposition chain on the symmetric group $S_{n}$ with a regular parameter vector $p = (p_{i, j})_{i \neq = j}$ . Fill's spectral gap conjecture, r…

math.CO2025

On the chromatic number of random triangle-free graphs

Clayton Mizgerd, Will Perkins, Yuzhou Wang

We study the chromatic number of typical triangle-free graphs with $Θ (n^{3/2} (lo g n)^{1/2})$ edges and establish the width of the scaling window for the transitions…

math.CO2025

The random graph process is globally synchronizing

Vishesh Jain, Clayton Mizgerd, Mehtaab Sawhney

The homogeneous Kuramoto model on a graph $G = (V, E)$ is a network of $∣ V ∣$ identical oscillators, one at each vertex, where every oscillator is coupled bidirectionally (with unit…