Related papers: A Matrix Contraction Process
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
We investigate the probability of observing a given pattern of $n$ rises and falls in a random stationary data series. The data are modelled as a sequence of $n+1$ independent and identically distributed random numbers. This probabilistic…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…
We consider particles suspended in a randomly stirred or turbulent fluid. When effects of the inertia of the particles are significant, an initially uniform scatter of particles can cluster together. We analyse this 'unmixing' effect by…
Polymers in nonuniform flows undergo strong deformation, which in the presence of persistent stretching can result in the coil-stretch transition. This phenomenon has been characterized by using the formalism of nonequilibrium statistical…
We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the…
We consider advection of small inertial particles by a random fluid flow with a strong steady shear component. It is known that inertial particles suspended in a random flow can exhibit clusterization even if the flow is incompressible. We…
I study the product of independent identically distributed $D\times D$ random probability matrices. Some exact asymptotic results are obtained. I find that both the left and the right products approach exponentially to a probability…
We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
We present a new class of particle methods with deformable shapes that converge in the uniform norm without requiring remappings, extended overlapping or vanishing moments for the particles. The crux of the method is to use polynomial…
We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable…
Following the works by Wiegmann-Zabrodin, Elbau-Felder, Hedenmalm-Makarov, and others, we consider the normal matrix model with an arbitrary potential function, and explain how the problem of finding the support domain for the asymptotic…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
We introduce a simple but powerful technique to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to non conservative zero range processes on finite graphs, and to…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…