J. Marckert

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math.PR2025

Conditioning random points by the number of vertices of their convex hull: the bi-pointed case

Jean-FranÃ§ois Marckert, Ludovic Morin

Pick $N$ random points $U_{1}, \dots, U_{N}$ independently and uniformly in a triangle ABC with area 1, and take the convex hull of the set ${A, B, U_{1}, \dots, U_{N}}$ . The boundary of…

math.PR2025

A combinatorial perspective on the Kemeny constant and more

Luis Fredes, Jean-FranÃ§ois Marckert

Let $M$ be an irreducible transition matrix on a finite state space $V$ . For a Markov chain $C = (C_{k}, k \geq 0)$ with transition matrix $M$ , let $I ¨ _{u}^{\geq 1}$ denote the first posit…

math.PR2025

Dispersion models on a circle: universal properties and asymptotic results

Consider a sequence of masses $m_{0}, m_{1}, ...$ arriving uniformly at random at some points $u_{0}, u_{1}, ...$ on the unit circle $R / Z$ (or on $Z / n Z$ , in…

math.PR2024

Markov chains on trees: almost lower and upper directed cases

Luis Fredes, Jean-FranÃ§ois Marckert

The transition matrix of a Markov chain $(X_{k}, k \geq 0)$ on a finite or infinite rooted tree is said to be almost upper-directed if, given $X_{k}$ , the node $X_{k + 1}$ is either a desc…