91 citations · 275 across the 27 of their papers we have counts for
29 papers
Gaussian free field with logarithmic singularities and reduced Green's energy
Mingchang Liu, Titus Lupu, Hao Wu
We analyze the level lines of the Gaussian Free Field with logarithmic singularities in polygonal domains. We focus on the (none-zero) singular case and compare it to the singular-…
Renormalised two-point functions of CLE gaskets
Juhan Aru, Titus Lupu
We first consider nested CLE in a simply-connected domain and compute some exact renormalised probabilities: the probability that two points belong to the same CLE gasket a…
Three-dimensional Brownian loop soup clusters
Antoine Jego, Titus Lupu
We study Brownian loop soup clusters in for an arbitrary intensity . We show the existence of a phase transition for the presence of unbounded clusters and stud…
Intensity doubling for Brownian loop-soups in high dimensions
Titus Lupu, Wendelin Werner
We derive an intensity doubling feature of critical Brownian loop-soups on the cable-graphs of for that can be described as follows: In the box $[-N, N]^d…
Relation between Wick powers and excursion clusters of the 2D GFF
Titus Lupu
We study the decomposition of the Wick powers of the continuum GFF in dimension via the first passage sets (FPS) and the excursion clusters (sign components) of the GFF. These…
The height gap of planar Brownian motion is
Antoine Jego, Titus Lupu, Wei Qian
We show that the occupation measure of planar Brownian motion exhibits a constant height gap of across its outer boundary. This property bears similarities with the celebrate…
Conformally invariant fields out of Brownian loop soups
Antoine Jego, Titus Lupu, Wei Qian
Consider a Brownian loop soup with subcritical intensity in some 2D bounded simply connected domain. We define and study the properties of a confor…
Excursion decomposition of the 2D continuum GFF
Juhan Aru, Titus Lupu, Avelio Sepúlveda
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 t…
Crossing exponent in the Brownian loop soup
Antoine Jego, Titus Lupu, Wei Qian
We study the clusters of loops in a Brownian loop soup in some bounded two-dimensional domain with subcritical intensity . We obtain an exact expression for the asymp…
An equivalence between gauge-twisted and topologically conditioned scalar Gaussian free fields
Titus Lupu
We study on the metric graphs two types of scalar Gaussian free fields (GFF), the usual one and the one twisted by a -valued gauge field. We show that the latter can be o…
Multiplicative chaos of the Brownian loop soup
Élie Aïdékon, Nathanaël Berestycki, Antoine Jego +1
We construct a measure on the thick points of a Brownian loop soup in a bounded domain D of the plane with given intensity , which is formally obtained by exponentiating the s…
A level line of the Gaussian free field with measure-valued boundary conditions
Titus Lupu, Hao Wu
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 contin…
Isomorphisms of -Dyson's Brownian motion with Brownian local time
Titus Lupu
We show that the Brydges-Fröhlich-Spencer-Dynkin and the Le Jan's isomorphisms between the Gaussian free fields and the occupation times of symmetric Markov processes generalize to…
Extremal distance and conformal radius of a CLE_4 loop
Juhan Aru, Titus Lupu, Avelio Sepúlveda
Consider CLE in the unit disk and let be the loop of the CLE surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen fr…
Inverting the Ray-Knight identity on the line
Titus Lupu, Christophe Sabot, Pierre Tarrès
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 invol…
Topological expansion in isomorphism theorems between matrix-valued fields and random walks
Titus Lupu
We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fiel…
The first passage sets of the 2D Gaussian free field: convergence and isomorphisms
Juhan Aru, Titus Lupu, Avelio Sepúlveda
In a previous article, we introduced the first passage set (FPS) of constant level of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. In…
Fine mesh limit of the VRJP in dimension one and Bass-Burdzy flow
Titus Lupu, Christophe Sabot, Pierre Tarrès
We introduce a continuous space limit of the Vertex Reinforced Jump Process (VRJP) in dimension one, which we call Linearly Reinforced Motion (LRM) on . It is constructed out o…
First passage sets of the 2D continuum Gaussian free field
Juhan Aru, Titus Lupu, Avelio Sepúlveda
We introduce the first passage set (FPS) of constant level of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set…
Inverting the coupling of the signed Gausssian free field with a loop soup
Titus Lupu, Christophe Sabot, Pierre Tarrès
Lupu introduced a coupling between a random walk loop-soup and a Gaussian free field, where the sign of the field is constant on each cluster of loops. This coupling is a signed ve…
The random pseudo-metric on a graph defined via the zero-set of the Gaussian free field on its metric graph
Titus Lupu, Wendelin Werner
We further investigate properties of the Gaussian free field (GFF) on the metric graph associated to a discrete weighted graph (where the edges of the latter are replaced by contin…
A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field
Titus Lupu, Wendelin Werner
We make a few elementary observations that relate directly the items mentioned in the title. In particular, we note that when one superimposes the random current model related to t…
Convergence of the two-dimensional random walk loop soup clusters to CLE
Titus Lupu
We consider the random walk loop soup on the discrete half-plane corresponding to a central charge c in (0, 1]. We look at the clusters of discrete loops and show that the scaling…
Loop percolation on discrete half-plane
Titus Lupu
We consider the random walk loop soup on the discrete half-plane and study the percolation problem, i.e. the existence of an infinite cluster of loops. We show that the critical va…