Related papers: Sign-time distributions for interface growth

In this paper we consider a class of non-local in time telegraph equations. Recently, it has been proved that the fundamental solutions of such equations can be interpreted as the probability density function of a stochastic process. We…

We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…

A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [L. H. Tang and H. Leschhorn, Phys. Rev. A {\bf 45}, R8309 (1992)]. The evolution equation for the height, the mean height, and…

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…

We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the…

We propose moment relaxations for data-driven Wasserstein distributionally robust optimization problems. Conditions are identified to ensure asymptotic consistency of such relaxations for both single-stage and two-stage problems, together…

In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…

This paper is a short review of the connection between certain types of growth processes and the integrable systems theory, written from the viewpoint of the latter. Starting from the dispersionless Lax equations for the 2D Toda hierarchy,…

Recent developments on large-scale distributed machine learning applications, e.g., deep neural networks, benefit enormously from the advances in distributed non-convex optimization techniques, e.g., distributed Stochastic Gradient Descent…

We develop a model of string dynamics with back-reaction from both scaling and non-scaling loops taken into account. The evolution of a string network is described by the distribution functions of coherence segments and kinks. We derive two…

Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…

This paper proposes distributed discrete-time algorithms to cooperatively solve an additive cost optimization problem in multi-agent networks. The striking feature lies in the use of only the sign of relative state information between…

We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only considering domain growth and not the interface curvature.…

Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…

Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…

A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…

We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-slopes (interfacial) theories and the interplay between the…

The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…