Related papers: Determinantal point processes conditioned on rando…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We propose discrete determinantal point processes (DPPs) for priors on the model parameter in Bayesian variable selection. By our variable selection method, collinear predictors are less likely to be selected simultaneously because of the…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function {\psi}. We obtain the asymptotic behavior of the…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified…
We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for the associated Jacobi matrices. For classical weights, we show…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in many applications where diversity is desired. While DPPs have many appealing properties, such as efficient sampling, learning the…
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
Determinantal point processes on a measure space X whose kernels represent trace class Hermitian operators on L^2(X) are associated to "quasifree" density operators on the Fock space over L^2(X).
We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with sequential update. The joint distribution of the positions of selected particles is expressed as a Fredholm determinant with a kernel defining a…
Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…