Author

G. Kozma

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Preprint Sep 2026

Galois groups of random polynomials of large degree

We study random polynomials of the form $R(x)=x^n+\omega_{n-1}x^{n-1}+\cdots+\omega_0$, where $\omega_0,\dots,\omega_{n-1}$ are independent, uniformly bounded integer-valued random variables, and $\omega_1,\dots,\omega_{n-1}$ have a fixed common law $\mu$. We prove (unconditionally) that, if the R\'{e}nyi entropy of or...

Guy Blachar, E. Breuillard, G. Kozma · 0 citations

Open access Mar 2023

The Number of Tiles of $\mathbb{Z}^d$

For fixed $d\ge 1$, let $t_{n,d}$ be the number of subsets of$[n]^d$ that tile $\mathbb{Z}^d$ by translations. We prove that\[t_{n,d}=(3^{1/3})^{n^d\pm o(n^d)}.\]

I. Benjamini, G. Kozma, Elad Tzalik · Electronic Journal of Combin... · 0 citations