Related papers: Scaling limits for exploration algorithms

Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

The problem of pure exploration in Markov decision processes has been cast as maximizing the entropy over the state distribution induced by the agent's policy, an objective that has been extensively studied. However, little attention has…

We study a simple model of algorithmic collusion in which Q-learning algorithms are designed in a strategic fashion. We let players (\textit{designers}) choose their exploration policy simultaneously prior to letting their algorithms…

We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit…

We obtain scaling limit results for asymmetric trap models and their infinite volume counterparts, namely asymmetric K processes. Aging results for the latter processes are derived therefrom.

The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…

We consider the general physical situation of a quantum system $\H_0$ interacting with a chain of exterior systems $\bigotimes_\N \H$, one after the other, during a small interval of time $h$ and following some Hamiltonian $H$ on $\H_0…

We introduce a class of absorption mechanisms and study the behavior of real-valued centered random walks with finite variance that do not get absorbed. In particular, we prove persistence and scaling limit results, which, in many cases of…

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…

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…

We consider certain noncolliding interacting particle systems driven by Brownian noise. A key example is drifted Brownian motions conditioned not to intersect and related models of eigenvalues of Hermitian random matrices. We establish…

In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…

We are interested in the cycles obtained by slicing at all heights random Boltzmann triangulations with a simple boundary. We establish a functional invariance principle for the lengths of these cycles, appropriately rescaled, as the size…

Optimization algorithms are increasingly being used in applications with limited time budgets. In many real-time and embedded scenarios, only a few iterations can be performed and traditional convergence metrics cannot be used to evaluate…

We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…

We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…

We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…