Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Lupu, Titus"'
We show that the occupation measure of planar Brownian motion exhibits a constant height gap of $5/\pi$ across its outer boundary. This property bears similarities with the celebrated results of Schramm--Sheffield [18] and Miller--Sheffield [12] conc
Externí odkaz:
http://arxiv.org/abs/2403.03040
Consider a Brownian loop soup $\mathcal{L}_D^\theta$ with subcritical intensity $\theta \in (0,1/2]$ in some 2D bounded simply connected domain. We define and study the properties of a conformally invariant field $h_\theta$ naturally associated to $\
Externí odkaz:
http://arxiv.org/abs/2307.10740
In this note we show that the 2D continuum Gaussian free field (GFF) admits an excursion decomposition that is on the one hand similar to the classical excursion decomposition of the Brownian motion, and on the other hand can be seen as an FK represe
Externí odkaz:
http://arxiv.org/abs/2304.03150
We study the clusters of loops in a Brownian loop soup in some bounded two-dimensional domain with subcritical intensity $\theta \in (0,1/2]$. We obtain an exact expression for the asymptotic probability of the existence of a cluster crossing a given
Externí odkaz:
http://arxiv.org/abs/2303.03782
Autor:
Lupu, Titus
We study on the metric graphs two types of scalar Gaussian free fields (GFF), the usual one and the one twisted by a $\{-1,1\}$-valued gauge field. We show that the latter can be obtained, up to an additional deterministic transformation, by conditio
Externí odkaz:
http://arxiv.org/abs/2209.07901
Publikováno v:
Proceedings of the London Mathematical Society 126 (4), 1254-1393, 2023
We construct a measure on the thick points of a Brownian loop soup in a bounded domain D of the plane with given intensity $\theta>0$, which is formally obtained by exponentiating the square root of its occupation field. The measure is constructed vi
Externí odkaz:
http://arxiv.org/abs/2107.13340
Autor:
Lupu, Titus, Wu, Hao
Publikováno v:
Science China Mathematics 2023
In this article, we construct samples of SLE-like curves out of samples of CLE and Poisson point process of Brownian excursions. We show that the law of these curves depends continuously on the intensity measure of the Brownian excursions. Using such
Externí odkaz:
http://arxiv.org/abs/2106.15169
Autor:
Lupu, Titus
Publikováno v:
Electronic Journal of Probability 26, 1-31, 2021
We show that the Brydges-Fr\"ohlich-Spencer-Dynkin and the Le Jan's isomorphisms between the Gaussian free fields and the occupation times of symmetric Markov processes generalize to the $\beta$-Dyson's Brownian motion. For $\beta\in\{1,2,4\}$ this i
Externí odkaz:
http://arxiv.org/abs/2009.03026
Publikováno v:
The Annals of Probability 50 (2), 509-558, 2022
Consider CLE$_4$ in the unit disk and let $\ell$ be the loop of the CLE$_4$ surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by $\ell$. We complement their
Externí odkaz:
http://arxiv.org/abs/2004.13570
Publikováno v:
Electronic Journal of Probability 26, 1-25, 2021
Using a divergent Bass-Burdzy flow we construct a self-repelling one-dimensional diffusion. Heuristically, it can be interpreted as a solution to an SDE with a singular drift involving a derivative of the local time. We show that this self-repelling
Externí odkaz:
http://arxiv.org/abs/1910.06836