Related papers: Notes on the occupancy problem with infinitely man…
In many natural situations one observes a local system with many competing species which is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When…
With the internet, a massive amount of information on species abundance can be collected under citizen science programs. However, these data are often difficult to use directly in statistical inference, as their collection is generally…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
We have studied both clusters and bulk systems while investigating amorphous states. We have varied the nature of interaction amongst the particles of the system under consideration in order to reveal the possible presence of universality…
For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied…
One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances…
We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community…
Consider a number, finite or not, of urns each with fixed capacity $r$ and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain $r$ balls. When $r=1$, using analytic…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
We study a resource allocation setting where $m$ discrete items are to be divided among $n$ agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common…
We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by ratios of consecutive elements in orbits. Assuming the…
We study the time evolution of occupation numbers for interacting Fermi-particles in the situation when exact compound states are "chaotic". This situation is generic for highly excited many-particles states in heavy nuclei, complex atoms,…
We consider the Moran process with two populations competing under an iterated Prisoners' Dilemma in the presence of mutation, and concentrate on the case where there are multiple Evolutionarily Stable Strategies. We perform a complete…
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…
We show that the fluctuations of the periodic orbits of deterministically chaotic systems can be captured by supersymmetry, in the sense that they are repackaged in the contribution of the absolute value of the determinant of the noise…
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…
We find the asymptotic total variation distance between two distributions on configurations of m balls in n labeled bins: in the first, each ball is placed in a bin uniformly at random; in the second, k balls are planted in an arbitrary but…
We consider positive entropy $G$-systems for certain countable, discrete, infinite left-orderable amenable groups $G$. By undertaking local analysis, the existence of asymptotic pairs and chaotic sets will be studied in connecting with the…
The random flights are (continuous time) random walkswith finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the…