Related papers: On intermediate levels of nested occupancy scheme …
Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been…
The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted…
Consider two urns, $A$ and $B$, where initially $A$ contains a large number $n$ of balls and $B$ is empty. At each step, with equal probability, either we pick a ball at random in $A$ and place it in $B$, or vice-versa (provided of course…
A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The…
We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set.…
Modeling non-stationary data is a challenging problem in the field of continual learning, and data distribution shifts may result in negative consequences on the performance of a machine learning model. Classic learning tools are often…
We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that…
We extend the $N$ branching Brownian motions model of population invasion to higher-order asexual reproduction. Increasing reproduction order leads to qualitative changes: invasion fronts generically cease to exist beyond binary…
Let $(\xi_k,\eta_k)_{k\in\mathbb{N}}$ be independent identically distributed random vectors with arbitrarily dependent positive components. We call a (globally) perturbed random walk a random sequence $(T_k)_{k\in\mathbb{N}}$ defined by…
Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyze this phenomenon, we note that invaders often cluster spatially when rare, and…
The coordinate and momentum space configurations of the net baryon number in heavy ion collisions that undergo spinodal decomposition, due to a first-order phase transition, are investigated using state-of-the-art machine-learning methods.…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…
In arbitrary spatial dimension $d\ge 1$, we study a generalized model of random walks in a time-varying random environment (RWRE) defined by a stochastic flow of kernels. We consider the quenched probability distribution of the random…
We consider the statistics of occupation times, the number of visits at the origin and the survival probability for a wide class of stochastic processes, which can be classified as renewal processes. We show that the distribution of these…
Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
The paper investigates theoretical issues in applying the universal swarming technique to efficient content distribution. In a swarming session, a file is distributed to all the receivers by having all the nodes in the session exchange file…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…