Related papers: Observables of Macdonald processes
In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process where each particle is removed…
The paper deals with renewal theory for a class of extremal Markov sequences connected with the Kendall convolution. We consider here some particular cases of the Wold processes associated with generalized convolutions. We prove an analogue…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…
We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process can be expressed in terms of determinants of…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We study Fredholm determinants related to a family of kernels which describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher order analogues of the Airy kernel and are…
The purpose of this article is to develop a theory behind the occurrence of "path-integral" kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants…
Point processes are probabilistic tools for modeling event data. While there exists a fast-growing literature studying the relationships between point processes, it remains unexplored how such relationships connect to causal effects. In the…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…
The diagonal spin-spin correlations of the square lattice Ising model, originally expressed as Toeplitz determinants, are given by two distinct Fredholm determinants - one with an integral operator having an Appell function kernel and…
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for the Macdonald functions.
We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an…
We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and non-intersecting paths models. By relating the logarithmic derivatives of the…
Estimation of the four generalized lambda distribution parameters is not straightforward, and available estimators that perform best have large computation times. In this paper, we introduce a simple two-step estimator of the parameters…
An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood…
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…