Related papers: Scaling limit of a discrete prion dynamics model
We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…
We derive a linear recursion relation for the species abundance distribution in a statistical model of ecology and demonstrate the existence of a scaling solution.
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
We study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in micro-fluidic micro-models of porous media.…
Using Mickens nonstandard method, we obtain a discrete family of nonautonomous eco-epidemiological models that include general functions corresponding to the predation of the infected and uninfected preys. We obtain results on the…
We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth and is also…
We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit…
The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical…
The idea that there are any large-scale trends in the evolution of biological organisms is highly controversial. It is commonly believed, for example, that there is a large-scale trend in evolution towards increasing complexity, but…
We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation…
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that…
We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the…
Motivated by mapping from a stochastic system with spatially random rates, we consider disordered non-conserving free-fermion systems using a scaling procedure for the equations of motion. This approach demonstrates disorder-induced…
A discrete drift-diffusion model is derived from a microscopic sequential tunneling model of charge transport in weakly coupled superlattices provided temperatures are low or high enough. Realistic transport coefficients and novel contact…
In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the…
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding…
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We consider a model for the polymerization (fragmentation) process involved in infectious prion self-replication and study both its dynamics and non-zero steady state. We address several issues. Firstly, we give conditions leading to size…
A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of hydrodynamic scaling limit of…