Related papers: A random model of publication activity
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…
This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…
In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…
We propose and study a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows the weights of links are…
Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…
We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Motivated by applications in mathematical biology concerning randomly alternating motion of micro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are…
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is…
Random walks on a group $G$ model many natural phenomena. A random walk is defined by a probability measure $p$ on $G$. We are interested in asymptotic properties of the random walks and in particular in the linear drift and the asymptotic…
We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero.…
We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a…
In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
We consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of…
We study the asymptotic behaviour of the probability that a weighted sum of centered i.i.d. random variables X_k does not exceed a constant barrier. For regular random walks, the results follow easily from classical fluctuation theory,…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…