G. Perarnau

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math.PR2026

The temporal stochastic block model

Sofiya Burova, GÃ¡bor Lugosi, Guillem Perarnau

Motivated by the need to understand infection spreading in inhomogeneous populations, we consider a \emph{temporal} version of the stochastic block model, where each edge is equipp…

math.PR2026

Composition of random functions and word reconstruction

Guillaume Chapuy, Guillem Perarnau

Given two functions $a : [n] \to [n]$ and $b : [n] \to [n]$ chosen uniformly at random, any word $w = w_{1} w_{2} \dots w_{k} \in {a, b}^{k}$ induces a…

math.PR2025

An elementary proof of the bunkbed conjecture for forests

Serte Donderwinkel, Joost Jorritsma, Guillem Perarnau

Although false for general graphs, this note gives an elementary proof of the bunkbed conjecture for any acyclic graph. The argument is short and self-contained, and may be of educ…

math.PR2025

Minimum stationary values of sparse random directed graphs

Xing Shi Cai, Guillem Perarnau

We consider the stationary distribution of the simple random walk on the directed configuration model with bounded degrees. Provided that the minimum out-degree is at least $2$ , wi…