Related papers: Majority dynamics on finite trees

We establish finite time extinction with probability one for weak solutions of the Cauchy-Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum.…

We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term…

We subject the phenomenologically successful large volume scenario of hep-th/0502058 to a first consistency check in string theory. In particular, we consider whether the expansion of the string effective action is consistent in the…

Consider a dynamical system $T:\mathbb{T}\times \mathbb{R}^{d} \rightarrow \mathbb{T}\times \mathbb{R}^{d} $ given by $ T(x,y) = (E(x), C(y) + f(x))$, where $E$ is a linear expanding map of $\mathbb{T}$, $C$ is a linear contracting map of…

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…

Inferring the ancestral state at the root of a phylogenetic tree from states observed at the leaves is a problem arising in evolutionary biology. The simplest technique -- majority rule -- estimates the root state by the most frequently…

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…

Consider a rooted tree $T$ with leaf-set $[n]$, and with all non-leaf vertices having out-degree $2$, at least. A rooted tree $\mathcal T$ with leaf-set $S\subset [n]$ is induced by $S$ in $T$ if $\mathcal T$ is the lowest common ancestor…

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…

This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…

In this article, we introduce Brownian motion on stable looptrees using resistance techniques. We prove an invariance principle characterising it as the scaling limit of random walks on discrete looptrees, and prove precise local and global…

This paper presents two new deterministic algorithms for constructing consensus trees. Given an input of k phylogenetic trees with identical leaf label sets and n leaves each, the first algorithm constructs the majority rule (+) consensus…

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little…

A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…

Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…

We consider the following degenerate half wave equation on the one dimensional torus $$\quad i\partial_t u-|D|u=|u|^2u, \; u(0,\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a…

We consider systems of stochastic evolutionary equations of the type $$du=\mathrm{div}\,S(\nabla u)\,dt+\Phi(u)dW_t$$ where $S$ is a non-linear operator, for instance the $p$-Laplacian $$S(\xi)=(1+|\xi|)^{p-2}\xi,\quad \xi\in\mathbb…

In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…

We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d_0 such that, for any d \geq d_0, the set of parameter values…