Benny Sudakov

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20242026

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math.PR2026

Distinguishability threshold for random geometric graphs

Zach Hunter, Aleksa MilojeviÄ, Benny Sudakov

The spherical random geometric graph $G (n, d, p)$ is obtained by sampling $n$ independent points uniformly on the unit sphere $S^{d - 1} \subseteq R^{d}$ and joining pair…

math.PR2026

On the Probability a Weighted Bernoulli Sum Exceeds Its Mean

Aleksa Milojevic, Benny Sudakov

Let $w_{1}, \dots, w_{m}$ be positive real weights whose sum is $1$ , and let $v_{1}, \dots, v_{m}$ be i.i.d. Bernoulli $(p)$ random variables. If we let $X = \sum_{i = 1}^{m} w_{i} v_{i}$ , then we co…

math.PR2026

Supercritical sharpness of percolation

Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan +2

We prove that for supercritical percolation on every infinite transitive graph, the probability that the origin belongs to a finite cluster of size at least $n$ decays exponentiall…