Related papers: Multiple SLE type scaling limits: from local to gl…

We study random $k$-connected chordal graphs with bounded tree-width. Our main results are scaling limits and quenched local limits.

Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…

In discrete convex analysis, the scaling and proximity properties for the class of L$^\natural$-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of…

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.…

This work introduces a construction of conformal processes that combines the theory of branching processes with chordal Loewner evolution. The main novelty lies in the choice of driving measure for the Loewner evolution: given a finite…

Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…

It was recently proposed in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro & Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of the infinite plane 2d critical Ising model for finite…

We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…

We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…

In the last few years, new insights have permitted unexpected progress in the study of fractal shapes in two dimensions. A new approach, called Schramm-Loewner evolution, or SLE, has arisen through analytic function theory and probability…

In this article we show the convergence of a loop ensemble of interfaces in the FK Ising model at criticality, as the lattice mesh tends to zero, to a unique conformally invariant scaling limit. The discrete loop ensemble is described by a…

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of…

The Stochastic Loewner equation, introduced by Schramm, gives us a powerful way to study and classify critical random curves and interfaces in two-dimensional statistical mechanics. New kind of stochastic Loewner equation, called fractional…

The Schramm-Loewner evolution (SLE_\kappa) is a candidate for the scaling limit of random curves arising in two-dimensional critical phenomena. When \kappa < 8, an instance of SLE_\kappa is a random planar curve with almost sure Hausdorff…

We consider maps which are constructed from plane trees by assigning marks to the corners of each vertex and then connecting each pair of consecutive marks on their contour by a single edge. A measure is defined on the set of such maps by…

After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…