Related papers: Scaling limit of a discrete prion dynamics model

We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…

We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…

We solve exactly the general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical…

We prove that the scaling limit of the continuous solid-on-solid model in $\mathbb{Z}^d$ is a multiple of the Gaussian free field.

Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…

The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate…

We consider a family of growth models defined using conformal maps in which the local growth rate is determined by $|\Phi_n'|^{-\eta}$, where $\Phi_n$ is the aggregate map for $n$ particles. We establish a scaling limit result in which…

Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…

One of the classical questions in evolutionary biology is how evolutionary processes are coupled at the gene and species level. With this motivation, we compare the topological properties (mainly the depth scaling, as a characterization of…

We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…

Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

There are many different models--both continuous and discrete--used to describe gene mutation fixation. In particular, the Moran process, the Kimura equation and the replicator dynamics are all well known models, that might lead to…

At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…

We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…

We propose a novel approach to continuum modelling of 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…

Going from a scaling approach for birth/death processes, we investigate the scaling limit of solutions to non-Markovian stochastic control problems by studying the convergence of solutions to BSDEs driven a sequence of converging…

The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…

We consider a shot-noise field defined on a stationary determinantal point process on $\mathbb{R}^d$ associated with i.i.d. amplitudes and a bounded response function, for which we investigate the scaling limits as the intensity of the…

We introduce generalizations of Aldous' Brownian Continuous Random Tree as scaling limits for multicritical models of discrete trees. These discrete models involve trees with fine-tuned vertex-dependent weights ensuring a k-th root…