Related papers: Large-deviation properties of the extended Moran m…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
This paper studies the spatial coalescent on $\Z^2$. In our setting, the partition elements are located at the sites of $\Z^2$ and undergo local delayed coalescence and migration. That is, pairs of partition elements located at the same…
We analyze the geometry of the species- and genotype-size distribution in evolving and adapting populations of single-stranded self-replicating genomes: here programs in the Avida world. We find that a scale-free distribution (power law)…
We present large deviations principles for the moments of the empirical spectral measure of Wigner matrices and empirical measure of $\beta$-ensembles in three cases : the case of Wigner matrices without Gaussian tails, that is Wigner…
Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy…
We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…
In this paper we consider the two-type Moran model with $N$ individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution ${\mathbb P}$ on ${\mathbb R}_+$, and a type, either $1$ or $0$.…
We employ distribution regression (DR) to estimate the joint distribution of two outcome variables conditional on chosen covariates. While Bivariate Distribution Regression (BDR) is useful in a variety of settings, it is particularly…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
We consider a $\mathbb{R}^d$-valued branching random walk with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. With the help of the…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
We investigate the limiting behavior of sample central moments, examining the special cases where the limiting (as the sample size tends to infinity) distribution is degenerate. Parent (non-degenerate) distributions with this property are…
Exponential, and not Gaussian, decay of probability density functions was studied by Laplace in the context of his analysis of errors. Such Laplace propagators for the diffusive motion of single particles in disordered media were recently…
Configurational arrangement of network architecture and interaction character of individuals are two most influential factors on the mechanisms underlying the evolutionary outcome of cooperation, which is explained by the well-established…
Survey data are widely used to study how income inequality, poverty, and welfare evolve over time. A common practice is to estimate the income distribution separately for each year, treating annual observations as independent…
We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this…