Related papers: Random planar maps & growth-fragmentations

The aim of this paper is to present a self-similar growth-fragmentation process linked to a Brownian excursion in the upper half-plane $\mathbb{H}$, obtained by cutting the excursion at horizontal levels. We prove that the associated…

We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…

We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution on a space of trees is said to be self-similar if it is invariant with respect to the operation of pruning, which cuts…

The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…

Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the…

The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.

In this paper, we are interested in the self-similar growth-fragmentation process that shows up when slicing half-space excursions of a $d$-dimensional Brownian motion from hyperplanes. Such a family of processes turns out to be a spatial…

The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…

We revisit, in a self contained way, the Markov property on planar maps and decorated planar maps from three perspectives. First, we characterize the laws on these planar maps that satisfy both the Markov property and rerooting invariance,…

This paper is concerned mainly with the macroscopic fractal behavior of various random sets that arise in modern and classical probability theory. Among other things, it is shown here that the macroscopic behavior of Boolean coverage…

We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum…

We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local…

Growth-fragmentation processes model the evolution of positive masses which undergo binary divisions. The aim of this paper is twofold. First, we extend the theory of growth-fragmentation processes to allow signed mass. Among others, we…

We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…

We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In our model, each copy of the random field in the aggregation is built from two correlated one-dimensional random…

Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in…

We study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We…

We study Bernoulli percolations on random lattices of the half-plane obtained as local limit of uniform planar triangulations or quadrangulations. Using the characteristic spatial Markov property or peeling process of these random lattices…