Related papers: Fluctuations provide strong selection in Ostwald r…
This paper investigates optimal fluctuations for chemical reaction systems with N species, M reactions, and general rate law. In the limit of large volume, large fluctuations for such models occur with overwhelming probability in the…
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
In this paper, we study the precise late-time asymptotic behaviour of small data solutions for the Vlasov-Poisson system in dimension three. First, we show that the spatial density and the force field satisfy asymptotic self-similar…
We analyze the fluctuations of the dissipated energy in a simple and general model where dissipation, diffusion and driving are the key ingredients. The large deviation function for the dissipation follows from hydrodynamic fluctuation…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…
The well-posedness and regularity estimates in initial distributions are derived for singular McKean-Vlasov SDEs, where the drift contains a locally standard integrable term and a superlinear term in the spatial variable, and is Lipchitz…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
Sea ice is not continuous and homogeneous on large scales. Its morphology is inherently discrete and made of individual floes. In recent years, sea ice models have incorporated this horizontal heterogeneity. The modelling framework…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts…
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
The fluctuation theorem (FT), the first derived consequence of the {\it Chaotic Hypothesis} (CH) of ref. [GC1], can be considered as an extension to arbitrary forcing fields of the fluctuation dissipation theorem (FD) and the corresponding…
We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here we give strong theoretical foundations for the origins and abundance of Taylor's FS in different…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…