Related papers: Decomposition of Brownian loop-soup clusters
We show that if one conditions a cluster in a Brownian loop-soup $L$ (of any intensity) in a two-dimensional domain by a portion $l$ of its outer boundary, then in the remaining domain, the union of all the loops of $L$ that touch $l$…
The two-dimensional Brownian loop-soup is a Poissonian random collection of loops in a planar domain with an intensity parameter c. When c is not greater than 1, we show that the outer boundaries of the loop clusters are disjoint simple…
We derive an intensity doubling feature of critical Brownian loop-soups on the cable-graphs of ${\mathbb Z}^d$ for $d \ge 7$ that can be described as follows: In the box $[-N, N]^d$ (and with a probability that goes to $1$ as $N$ goes to…
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 the notion of indistinguishability of bosons. The properly…
We study Brownian loop soup clusters in $\mathbb{R}^3$ for an arbitrary intensity $\alpha>0$. We show the existence of a phase transition for the presence of unbounded clusters and study its basic properties. In particular, we show that,…
In this research announcement, we show that SLE curves can in fact be viewed as boundaries of certain simple Poissonian percolation clusters: Recall that the Brownian loop-soup (introduced in the paper arxiv:math.PR/0304419 with Greg…
We introduce a natural "massive" version of the Brownian loop soup of Lawler and Werner which displays conformal covariance and exponential decay. We show that this massive Brownian loop soup arises as the near-critical scaling limit of a…
For a Brownian loop soup with intensity $c\in(0,1]$ in the unit disk, we show that almost surely, the set of simple (resp. double) points on any portion of boundary of any of its clusters has Hausdorff dimension $2-\xi_c(2)$ (resp.…
For random collections of self-avoiding loops in two-dimensional domains, we define a simple and natural conformal restriction property that is conjecturally satisfied by the scaling limits of interfaces in models from statistical physics.…
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…
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…
The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete…
In this work, which is the first part of a series of two papers, we study the random walk loop soup in dimension two. More specifically, we estimate the probability that two large connected components of loops come close to each other, in…
We define and study a set of operators that compute statistical properties of the Brownian Loop Soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We…
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 between this loop soup and the usual loop soup conditioned…
We study Conformal Loop Ensemble (CLE$_{\kappa}$) in doubly connected domains: annuli, the punctured disc, and the punctured plane. We restrict attention to CLE$_{\kappa}$ for which the loops are simple, i.e. $\kappa\in (8/3,4]$. In the…
We show the result that is stated in the title of the paper, which has consequences about decomposition of Brownian loop-soup clusters in two dimensions.
We discuss the following type of results about critical Bernoulli percolation in high dimensions: The collection of clusters that do contain large (self-avoiding) loops in a large box is tight. The collection of these large loops has…
We study vertex-like operators built from the Brownian loop soup in the limit as the loop soup intensity tends to infinity. More precisely, following Camia, Gandolfi and Kleban (Nuclear Physics B 902, 2016), we take a Brownian loop soup in…
The loop clusters of a Poissonian ensemble of Markov loops on a finite or countable graph have been studied in \cite{Markovian-loop-clusters-on-graphs}. In the present article, we study the loop clusters associated with a rotation invariant…