相关论文: Exploration trees and conformal loop ensembles

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…

Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and…

Self-similar Markov trees constitute a remarkable family of random compact real trees carrying a decoration function that is positive on the skeleton. As the terminology suggests, they are self-similar objects that further satisfy a Markov…

Stochastic Loewner Evolutions (SLE) with a multiple sqrt(kappa)B of Brownian motion B as driving process are random planar curves (if kappa<=4) or growing compact sets generated by a curve (if kappa>4). We consider here more general Levy…

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…

The role of the conformal group in electrodynamics in four space-time dimensions is re-examined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with…

Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin. We do so…

We construct the COpula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork…

We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process…

We use the conformal group to study non-local operators in conformal field theories. A plane or a sphere (of any dimension) is mapped to itself by some subgroup of the conformal group, hence operators confined to that submanifold may be…

The development of Schramm--Loewner evolution (SLE) as the scaling limits of discrete models from statistical physics makes direct simulation of SLE an important task. The most common method, suggested by Marshall and Rohde \cite{MR05}, is…

Stochastic Loewner evolutions (SLE) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLE evolutions and conformal field theories (CFT) which is…

We extend unbounded Kasparov theory to encompass conformal group and quantum group equivariance. This new framework allows us to treat conformal actions on both manifolds and noncommutative spaces. As examples, we present unbounded…

This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees…

Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative…

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…

We consider uniform spanning tree (UST) in topological rectangles with alternating boundary conditions. The Peano curves associated to the UST converge weakly to hypergeometric SLE$_8$, denoted by hSLE$_8$. From the convergence result, we…

We consider a model of planar random aggregation from the ALE$(0,\eta)$ family where particles are attached preferentially in areas of low harmonic measure. We find that the model undergoes a phase transition in negative $\eta$, where for…

The Shcramm-Loewner evolution (SLE) is a correlated exploration process, in which for the chordal set up, the tip of the trace evolves in a self-avoiding manner towards the infinity. The resulting curves are named SLE$_{\kappa}$,…