Titus Lupu

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20182026

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math.PR2026

Three-dimensional Brownian loop soup clusters

Antoine Jego, Titus Lupu

We study Brownian loop soup clusters in $R^{3}$ for an arbitrary intensity $α > 0$ . We show the existence of a phase transition for the presence of unbounded clusters and stud…

math.PR2025

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 $Z^{d}$ for $d \geq 7$ that can be described as follows: In the box $[-N, N]^d…

math.PR2025

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 $2$ via the first passage sets (FPS) and the excursion clusters (sign components) of the GFF. These…

math.PR2018

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 $- a$ of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. In…

math.PR2018

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 $R$ . It is constructed out o…