Olivier Garet

collaborators

3 papers

math.PR2026

Probabilistic proof for non-survival at criticality : the Galton-Watson process and more

Olivier Garet

In a famous paper, Bezuidenhout and Grimmett demonstrated that the contact process dies out at the critical point.Their proof technique has often been used to study the growth of p…

math.CA2025

A simple master Theorem for discrete divide and conquer recurrences

Olivier Garet

The aim of this note is to provide a Master Theorem for some discrete divide and conquer recurrences: $X_{n} = a_{n} + j = 1 \sum m b_{j} X_{⌊ \frac{n}{m _{j}} ⌋},$ where the $m…

math.NT2025

How often is $x \mapsto x^{3}$ one-to-one in $Z / n Z$ ?

Olivier Garet

We characterize the integers n such that $x \mapsto x^{3}$ describes a bijection from the set $Z / n Z$ to itself and we determine the frequency of these integers. Prec…

Probabilistic proof for non-survival at criticality : the Galton-Watson process and more

A simple master Theorem for discrete divide and conquer recurrences

How often is x↦x3 one-to-one in Z/nZ?

How often is $x \mapsto x^{3}$ one-to-one in $Z / n Z$ ?