相关论文: 2D growth processes: SLE and Loewner chains

In the second article of this series, we establish the convergence of the loop ensemble of interfaces in the random cluster Ising model to a conformal loop ensemble (CLE) --- thus completely describing the scaling limit of the model in…

Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…

In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…

Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated…

Using their relationship with the free boson and the free symplectic fermion, we study the off-critical perturbation of SLE(4) and SLE(2) obtained by adding a mass term to the action. We compute the off-critical statistics of the source in…

Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…

We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…

One way to uniquely define Schramm-Loewner Evolution (SLE) in multiply connected domains is to use the restriction property. This gives an implicit definition of a $\sigma$-finite measure on curves; yet it is in general not clear how to…

We study the relationship between certain SLE$_\kappa(\rho)$ processes, which are variants of the Schramm-Loewner evolution with parameter $\kappa$ in which one keeps track of an extra marked point, and Liouville quantum gravity (LQG).…

Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…

We investigate the relation between the Laplacian-$b$ motion and stochastic Komatu-Loewner evolution (SKLE) on multiply connected subdomains of the upper half-plane, both of which are analogues to SLE. In particular, we show that, if the…

We revisit the topic of self-organized criticality (SOC) in simple statistical graph models, with the purpose of capturing essential processes leading to the emergence of macroscopic spacetime from the microscopic dynamics in loop quantum…

In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was discovered that a phase transition emerges on an…

We study random two-dimensional spanning forests in the plane that can be viewed both in the discrete case and in their appropriately taken scaling limits as a uniformly chosen spanning tree with some Poissonian deletion of edges or points.…

SLE(kappa,rho) is a generalisation of Schramm-Loewner evolution which describes planar curves which are statistically self-similar but not conformally invariant in the strict sense. We show that, in the context of boundary conformal field…

Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…

We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof of Cardy's formula, in order to determine…

The k-parent and infinite-parent spatial Lambda-Fleming Viot processes (or SLFV), introduced in Louvet (2023), form a family of stochastic models for spatially expanding populations. These processes are akin to a continuous-space version of…

Stochastic simulators are non-deterministic computer models which provide a different response each time they are run, even when the input parameters are held at fixed values. They arise when additional sources of uncertainty are affecting…

The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…