Related papers: SLE and alpha-SLE driven by Levy processes
L\'evy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an $\alpha$-stable law. For $\alpha < 1$, predictions from the physics literature suggest that high-dimensional L\'{e}vy matrices…
It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if $\kappa>4$ and a.s. cutpoints if $4<\kappa<8$. If $\kappa>4$, an appropriate version of $\SLE(\kappa)$ has a renewal property: it starts afresh after visiting…
We discuss the extension of radial SLE to multiply connected planar domains. First, we extend Loewner's theory of slit mappings to multiply connected domains by establishing the radial Komatu-Loewner equation, and show that a simple curve…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
We study in this paper the EM scheme for a family of well-posed critical SDEs with the drift $-x\log(1+|x|)$ and $\alpha$-stable noises. Specifically, we find that when the SDE is driven by a rotationally symmetric $\alpha$-stable processes…
In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results,…
We present the Levy's distributional property for symmetric Levy processes with generating triplet $(0, 0,\nu)$ or $(\sigma>0, \gamma, \nu)$ where $\nu$ is a symmetric measure on $R\backslash\{0\}$. This generalizes the classical Levy's…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
We provide a pedagogical review of CFT techniques to compute certain Schramm-Loewner Evolution (SLE) observables in the upper half-plane. The approach relies on the ability to express the observables as bulk-boundary correlation functions…
We study the stochastic transport equation with globally $\beta$-H\"older continuous and bounded vector field driven by a non-degenerate pure-jump L\'evy noise of $\alpha$-stable type. Whereas the deterministic transport equation may lack…
We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of…
We establish two results about local times of spectrally positive stable processes. The first is a general approximation result, uniform in space and on compact time intervals, in a model where each jump of the stable process may be marked…
Conformally-invariant curves that appear at critical points in two-dimensional statistical mechanics systems, and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm has invented a new rigorous…
The scaling limit of the spin cluster boundaries of the Ising model with domain wall boundary conditions is SLE with kappa=3. We hypothesise that the three-state Potts model with appropriate boundary conditions has spin cluster boundaries…
In this paper we consider a family of active scalars with a velocity field given by $u = \Lambda^{-1+\alpha}\nabla^{\perp} \theta$, for $\alpha \in (0,1)$. This family of equations is a more singular version of the two-dimensional Surface…
For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a…
The distributional support of the sample paths of L\'evy processes is an important issue for the construction of sparse statistical models, theories of integration in infinite dimensions and the existence of generalized solutions of…
We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally…
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We…
We show that a collection of independent Ising spins evolving stochastically can display surprisingly large fluctuations towards ordered behaviour, as quantified by certain types of time-integrated plaquette observables, despite the…