Related papers: Local weak limits for collapsed branching processe…
Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration…
Continuous-time Mallows processes are processes of random permutations of the set $\{1, \ldots, n\}$ whose marginal at time $t$ is the Mallows distribution with parameter $t$. Recently Corsini showed that there exists a unique Markov…
Continuous-time Bayesian networks (CTBNs) are graphical representations of multi-component continuous-time Markov processes as directed graphs. The edges in the network represent direct influences among components. The joint rate matrix of…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
Local branching is an improvement heuristic, developed within the context of branch-and-bound algorithms for MILPs, which has proved to be very effective in practice. For the binary case, it is based on defining a neighbourhood of the…
We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to…
In various scenarios motivated by real life, such as medical data analysis, autonomous driving, and adversarial training, we are interested in robust deep networks. A network is robust when a relatively small perturbation of the input…
We prove an invariance principle for a general class of continuous time critical branching processes with finite variance (non-local) branching mechanism. We show that the genealogical trees, viewed as random compact metric measure spaces,…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
The convergence of the Conjugate Gradient method is subject to a locality limitation which imposes a lower bound on the number of iterations required before a qualitatively accurate approximation can be obtained. This limitation originates…
Threshold rules of spreading in binary-state networks lead to cascades. We study persistent cascade-recovery dynamics on quasi-robust networks, i.e., networks which are robust against small trigger but may collapse for larger one. It is…
This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. The…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…
Recovering and reconstructing networks by accurately identifying missing and unreliable links is a vital task in the domain of network analysis and mining. In this article, by studying a specific local structure, namely a degree block…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
Biggins [Uniform convergence of martingales in the branching random walk. {\em Ann. Probab.}, 20(1):137--151, 1992] proved local uniform convergence of additive martingales in $d$-dimensional supercritical branching random walks at complex…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
We investigate the behavior of the empirical neighbourhood distribution of marked graphs in the framework of local weak convergence. We establish a large deviation principle for such families of empirical measures. The proof builds on…