Related papers: On the mean projection theorem for determinantal p…
We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.
We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…
We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent years. Sampling a determinantal point process however…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…
We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.
We prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that…
In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets…
We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an $\epsilon$-improvement in Kaufman's projection theorem for hyperplanes and an unconditional discretized radial projection theorem in the spirit…
This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…
We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function $f(x/R)$, as $R\to\infty$. We show that these functionals…
The first main result of this note, Theorem 1.2, establishes the determinantal identities (7) and (8) for the expectation, under a determinantal point process governed by an integrable projection kernel, of scaling limits of characteristic…