The first passage sets of the 2D Gaussian free field: convergence and isomorphisms
J Aru, T Lupu, A Sepúlveda - Communications in Mathematical Physics, 2020 - Springer
In a previous article, we introduced the first passage set (FPS) of constant level-aa of the two-
dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally …
dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally …
Conformally invariant fields out of Brownian loop soups
A Jego, T Lupu, W Qian - arXiv preprint arXiv:2307.10740, 2023 - arxiv.org
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 …
(0, 1/2] $ in some 2D bounded simply connected domain. We define and study the …
Excursion decomposition of the 2D continuum GFF
J Aru, T Lupu, A Sepúlveda - arXiv preprint arXiv:2304.03150, 2023 - arxiv.org
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 …
decomposition that is on the one hand similar to the classical excursion decomposition of …
Parity questions in critical planar Brownian loop-soups (or" where did the free planar bosons go?")
M Lehmkuehler, W Qian, W Werner - arXiv preprint arXiv:2403.07830, 2024 - arxiv.org
The critical two-dimensional Brownian loop-soup is an infinite collection of non-interacting
Brownian loops in a planar domain that possesses some combinatorial features related to …
Brownian loops in a planar domain that possesses some combinatorial features related to …
The height gap of planar Brownian motion is
A Jego, T Lupu, W Qian - arXiv preprint arXiv:2403.03040, 2024 - arxiv.org
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 …
gap of $5/\pi $ across its outer boundary. This property bears similarities with the celebrated …
Generalized disconnection exponents
W Qian - Probability Theory and Related Fields, 2021 - Springer
We introduce and compute the generalized disconnection exponents η _ κ (β) η κ (β) which
depend on κ ∈ (0, 4 κ∈(0, 4 and another real parameter β β, extending the Brownian …
depend on κ ∈ (0, 4 κ∈(0, 4 and another real parameter β β, extending the Brownian …
Cluster explorations of the loop soup on a metric graph related to the Gaussian free field
E Aidekon - arXiv preprint arXiv:2009.05120, 2020 - arxiv.org
We consider the loop soup at intensity ${1\over 2} $ conditioned on having local time $0 $
on a set of vertices with positive occupation field in their vicinities. We give a relation …
on a set of vertices with positive occupation field in their vicinities. We give a relation …
The height gap of planar Brownian motion is 5/π
A Jego, T Lupu, W Qian - 2024 - hal.science
We show that the occupation measure of planar Brownian motion exhibits a constant height
gap of 5/π across its outer boundary. This property bears similarities with the celebrated …
gap of 5/π across its outer boundary. This property bears similarities with the celebrated …