Tristan Guillaume

collaborators

4 papers

math.PR2026

Persistent Homology of the Wiener Sausage II: A Central Limit Theorem for Drifted Planar Brownian Motion

Tristan Guillaume

Let $X_{t} = B_{t} + μ t$ , $t \geq 0$ , be planar Brownian motion with nonzero drift, and let $K_{t}^{r} = {x \in R^{2} : dist (x, X [0, t]) \leq r}$ be the radius- $r$ Wiener sau…

math.PR2026

Persistence of the Wiener Sausage: Sampling Stability and a Law of Large Numbers for Drifted Planar Brownian Motion DRAFT -CURRENTLY UNDER REVIEW

Tristan Guillaume

We study the persistent homology of the offset filtration generated by the range of a planar Brownian motion with constant nonzero drift. The members of this filtration are the Wie…

math.PR2026

Exit times from time-dependent random domains: continuity, weak convergence, and exit-time profiles Draft -currently under review at Stochastic Processes and their Applications

Tristan Guillaume

We study exit times from time-dependent domains under joint perturbations of the trajectory and the domain. Representing a moving domain by a continuous barrier $Φ$ on space-time,…

math.PR2026

First Passage through a Continuous Barrier: Pathwise Decomposition, Random-Time Structure, and Compensators

Tristan Guillaume

Let t be the first-passage time of a continuous barrier by a c{à}dl{à}g adapted process. We show that t admits a canonical fourfold pathwise decomposition into continuous contact,…