Tristan Guillaume

collaborators

8 papers

math.PR2026

The joint exit time and exit location law of a planar Ornstein-Uhlenbeck process on annular sectors and principal axis rectangles

Tristan Guillaume

We study the first exit of an isotropic planar Ornstein-Uhlenbeck process from an annular sector, the region bounded by two concentric circular arcs and two radial segments, and ob…

cs.CG2026

Holes in planar parallel sets: An integrated Betti-number bound and its pointwise failure

Tristan Guillaume

Let A be a nonempty compact subset of the plane and let A (r) be its parallel set at distance r. We prove that the number of holes of A (r) the number of bounded components of its…

math.PR2026

Spectral-capacitary bounds for homological recovery from reflected Brownian trajectories

Tristan Guillaume

Can the topology of an unknown reflecting domain be recovered from one reflected Brownian trajectory, and how long must it be observed? We formulate this as a minimax homological i…

math.PR2026

The inradius law for the cavities of planar Brownian motion, with applications to the Wiener sausage

Tristan Guillaume

Let $K_{1} = B [0, 1]$ be the trace of a planar Brownian motion, and let $N_{in} (η)$ count the bounded components of $R^{2} ∖ K_{1}$ with inradius greater than $η$ .…

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 limit theorems for Betti-curve functionals of planar Brownian motion

Tristan Guillaume

We study the persistent homology of the offset filtration generated by the range of a planar Brownian motion with constant nonzero drift (Wiener sausages of increasing radius). We…

math.PR2026

Exit times from time-dependent random domains: continuity, weak convergence, and exit-time profiles

Tristan Guillaume

We study exit times from time-dependent domains under joint perturbations of the trajectory and the domain. Representing a moving domain as the negativity set of a continuous barri…

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,…