Related papers: Scaling limit for a drainage network model

Consider a family of random ordered graph trees $(T_n)_{n\geq 1}$, where $T_n$ has $n$ vertices. It has previously been established that if the associated search-depth processes converge to the normalised Brownian excursion when rescaled…

Recent research has tried to extend the concept of renormalization, which is naturally defined for geometric objects, to more general networks with arbitrary topology. The current attempts do not naturally apply to directed networks, for…

For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We…

Bandwidth-sharing networks as introduced by Massouli\'e & Roberts (1998) model the dynamic interaction among an evolving population of elastic flows competing for several links. With policies based on optimization procedures, such models…

We introduce a model of tree-rooted planar maps weighted by their number of $2$-connected blocks. We study its enumerative properties and prove that it undergoes a phase transition. We give the distribution of the size of the largest…

The Brownian web is a collection of coalescing Brownian motions started from every space-time point in R2. The Brownian web can be constructed as a scaling limit of coalescing one-dimensional simple random walks started at every point in a…

Accurate and scalable hydrologic models are essential building blocks of several important applications, from water resource management to timely flood warnings. However, as the climate changes, precipitation and rainfall-runoff pattern…

We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…

Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…

Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…

We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…

We show that the scaling limit of the random walk loop soup on suitable planar graphs is the Brownian loop soup, under a topology on multisets of unrooted, unparameterized, and macroscopic loops. The result holds assuming only convergence…

Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…

We propose a local strategy for constructing scale-free networks of arbitrary degree distributions, based on the redirection method of Krapivsky and Redner [Phys. Rev. E 63, 066123 (2001)]. Our method includes a set of external parameters…

This paper aims to measure the efficiency of urban street networks (a kind of complex networks) from the perspective of the multidimensional chain of connectivity (or flow). More specifically, we define two quantities: flow dimension and…

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In…

We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of…

We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…

In this paper, the scaling limit of random connected cubic planar graphs (respectively multigraphs) is shown to be the Brownian sphere. The proof consists in essentially two main steps. First, thanks to the known decomposition of cubic…