Isao Sauzedde

activity

20212026

collaborators

8 papers

math.PR2026

Functional central limit theorem for superdiffusive SDEs with stable noise

Aleksandar Mijatović, Andrey Pilipenko, Isao Sauzedde

This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $α$ -stable process.

math.PR2026

Brownian paths as loop-decorated SLEs

Nathanaël Berestycki, Isao Sauzedde

We construct an application, which takes as input a simple path and a possibly infinite collection of loops, and outputs a continuous path by adding the loops chronologically to th…

math.PR2024

Renormalised Amperean Area of Brownian Motions and Symanzik Representation of the 2D Abelian Yang--Mills--Higgs Field

Isao Sauzedde

We construct and study the renormalised Amperean area of a Brownian motion. First studied by W.Werner, the Amperean area is related to Lévy area and stochastic integrals in a way a…

math.PR2023

Brownian windings, Stochastic Green's formula and inhomogeneous magnetic impurities

Isao Sauzedde

We give a general Green formula for the planar Brownian motion, which we apply to study the Aharonov--Bohm effect induced by Poisson distributed magnetic impurities on a Brownian e…

math.PR2021

Winding and intersection of Brownian motions

Isao Sauzedde

We study the set of points $D_{n, m}$ around which two independent Brownian motions wind at least $n$ (resp. $m$ ) times. We prove that its area is asymptotically equivalen…

math.PR2021

Integration and stochastic integration in Gaussian multiplicative chaos

Isao Sauzedde

We show that for $γ < 4/3$ , it is possible to define the Levy area of a planar Brownian motion with the Liouville measure of intermittency parameter $γ$ as the underlying area…

math.PR2021

Lévy area without approximation

Isao Sauzedde

We give asymptotic estimations on the area of the sets of points with large Brownian winding, and study the average winding between a planar Brownian motion and a Poisson point pro…

math.PR2021

Planar Brownian motion winds evenly along its trajectory

Isao Sauzedde

Let $D_{N}$ be the set of points around which a planar Brownian motion winds at least $N$ times. We prove that the random measure on the plane with density $2 π N 1_{D_{N}}$ with respec…