Related papers: The Interacting Branching Process as a Simple Mode…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
We investigate solutions to the TAP equation, a phenomenological implementation of the Theory of the Adjacent Possible. Several implementations of TAP are studied, with potential applications in a range of topics including economics, social…
We consider inventions as novel combinations of existing technological capabilities. Patent data allow us to explicitly identify such combinatorial processes in invention activities. Unconsidered in the previous research, not every new…
We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the…
The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…
We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the…
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated…
Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects we devise an analytically solvable model…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
We introduce a simple open-ended model that describes the emergence of a shared vocabulary. The ordering transition toward consensus is generated only by an agreement mechanism. This interaction defines a finite and small number of states,…
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
We consider a population of $N$ individuals, of which we observe the number of actions as time evolves. For each couple of individuals $(i,j)$, $j$ may or not influence $i$, which we model by i.i.d. Bernoulli$(p)$-random variables, for some…