Related papers: Stochastic domination for the last passage percola…
In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the…
We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly…
We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We discuss a model for directed percolation in which the flux of material along each bond is a dynamical variable. The model includes a physically significant limiting case where the total flux of material is conserved. We show that the…
Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying…
In last passage percolation models, the energy of a path is maximized over all directed paths with given endpoints in a random environment, and the maximizing paths are called geodesics. The geodesics and their energy can be scaled so that…
We propose a general framework to study last passage times, suprema and drawdowns of a large class of stochastic processes. A central role in our approach is played by processes of class Sigma. After investigating convergence properties and…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
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…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
Study of the KPZ universality class has seen the emergence of universal objects over the past decade which arise as the scaling limit of the member models. One such object is the directed landscape, and it is known that exactly solvable…
Stochastic dominance is a technique for evaluating the performance of online algorithms that provides an intuitive, yet powerful stochastic order between the compared algorithms. Accordingly this holds for bijective analysis, which can be…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we show the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
We study the transition from stability to chaos in a dynamic last passage percolation model on $\mathbb{Z}^d$ with random weights at the vertices. Given an initial weight configuration at time $0$, we perturb the model over time in such a…
First passage percolation on $\mathbb{Z}^2$ is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage…