Related papers: Exploration processes and SLE$_6$

In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion limit aggregation (DLA) in the upper half plane with…

The paper studies processes defined on time domains structured as oriented spatial graphs (or metric graphs, or oriented branched 1-manifolds). This setting can be used, for example, for forecasting models involving branching scenarios. For…

Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…

Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…

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…

The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk…

We study the hunting process for a target, in which the hunter tracks the goal by smelling odors it emits. The odor intensity is supposed to decrease with the distance it diffuses. The Monte Carlo experiment is carried out on a…

We revisit the spatial ${\lambda}$-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the…

We prove a scaling limit theorem for the simple random walk on critical lattice trees in $\mathbb{Z}^d$, for $d\geq 8$. The scaling limit is the Brownian motion on the Integrated Super-Brownian Excursion (BISE) which is the same one that we…

This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site…

In recent work we have shown that loop-erased random walk (LERW) connecting two boundary points of a domain converges to the chordal Schramm-Loewner evolution (SLE(2)) in the sense of curves parametrized by Minkowski content. In this note…

We define a family of stochastic Loewner evolution-type processes in finitely connected domains, which are called continuous LERW (loop-erased random walk). A continuous LERW describes a random curve in a finitely connected domain that…

The peeling process is an algorithmic procedure that discovers a random planar map step by step. In generic cases such as the UIPT or the UIPQ, it is known [Curien & Le Gall, Scaling limits for the peeling process on random maps, Ann. Inst.…

We consider the scaling behavior of the range and $p$-multiple range, that is the number of points visited and the number of points visited exactly $p\geq 1$ times, of simple random walk on ${\mathbb Z}^d$, for dimensions $d\geq 2$, up to…

The third part of the paper concludes the proof of the main result --- the description of the ergodic decomposition of infinite Pickrell measures. First it is shown that the scaling limit of radial parts of finite-dimensional infinite…

We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

We consider discrete-time branching random walks with a radially symmetric distribution. Independently of each other individuals generate offspring whose relative locations are given by a copy of a radially symmetric point process…

We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…

Polar slice sampling, a Markov chain construction for approximate sampling, performs, under suitable assumptions on the target and initial distribution, provably independent of the state space dimension. We extend the aforementioned result…

This paper presents a numerical application of a self-consistent theory of partial redistribution in non-LTE conditions, developed in previous papers of the series. The code was described in a previous paper of this series. However, in that…