Related papers: Off-Criticality and the Massive Brownian Loop Soup

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 introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, $\beta$--corners…

We outline a strategy for showing convergence of loop-erased random walk on the Z^2 square lattice to SLE(2), in the supremum norm topology that takes the time parametrization of the curves into account. The discrete curves are parametrized…

Loop-erased random walk and it's scaling limit, Schramm--Loewner evolution, have found numerous applications in mathematics and physics. We present a 2 dimensional analogue of LERW, the loop erased random surface. We do this by defining a 2…

We establish universality for the largest singular values of products of random matrices with right unitarily invariant distributions, in a regime where the number of matrix factors and size of the matrices tend to infinity simultaneously.…

We introduce and study a new random surface which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed in arXiv:1401.3297. The law of the hyperbolic Brownian plane…

We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…

We construct a measure valued Markov process which we call infinite canonical super-Brownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian…

We develop a unified approach to establish the non-existence of three types of random fractals: (1) the pioneer triple points of the planar Brownian motion, answering an open question in [7], (2) the pioneer double cut points of the planar…

In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by the mating of two continuum random trees. In this paper, we…

We study the surface critical behavior of semi-infinite quenched random Ising-like systems at the special transition using three dimensional massive field theory up to the two-loop approximation. Besides, we extend up to the next-to leading…

We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of…

We study the critical and off-critical (Griffiths-McCoy) regions of the random transverse-field Ising spin chain by analytical and numerical methods and by phenomenological scaling considerations. Here we extend previous investigations to…

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on $\mathbb Z^d$, $d\ge 2$. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has…

We prove that properly rescaled large planar Eulerian triangulations converge to the Brownian map. This result requires more than a standard application of the methods that have been used to obtain the convergence of other families of…

We study a generalization of the Schramm-Loewner evolution loop measure to pairs of non-intersecting Jordan curves on the Riemann sphere. We also introduce four equivalent definitions for a two-loop Loewner potential: respectively…

Sources in higher representations of SU(N) gauge theory at T=0 couple with apparently stable strings with tensions depending on the specific representation rather than on its N-ality. Similarly at the deconfining temperature these sources…

We give a construction of an infinite stable looptree, which we denote by $\mathcal{L}_{\alpha}^{\infty}$, and prove that it arises both as a local limit of the compact stable looptrees of Curien and Kortchemski (2015), and as a scaling…

We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the…

Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theory and conformal field theory from the 1980s and 1990s. The…