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Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the…

We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…

Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…

By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corresponding spectral distances d_p on the set of all graphs.…

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Causal discovery algorithms based on probabilistic graphical models have emerged in geoscience applications for the identification and visualization of dynamical processes. The key idea is to learn the structure of a graphical model from…

Using the Palm measure notion, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific processes : stochastic subsets of Z^d, sets…

The assessment of the thermal properties of walls is essential for accurate building energy simulations that are needed to make effective energy-saving policies. These properties are usually investigated through in-situ measurements of…

In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as…

We show how to use a central limit approximation for additive co-cycles to describe non-equilibrium and far from equilibrium thermodynamic behavior. We consider first two weakly coupled Hamiltonian dynamical systems initially at different…

We present a general and convenient first principle method to study near-field radiative heat transfer. We show that the Landauer-like expression of heat flux can be expressed in terms of a frequency and wave-vector dependent macroscopic…

The problem of testing equality of the entire second order structure of two independent functional linear processes is considered. A fully functional $L^2$-type test is developed which evaluates, over all frequencies, the Hilbert-Schmidt…

Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are…

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…

We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of…

In this paper we develop statistical inference tools for high dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis…

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps…

Quantifying the similarity of two or more datasets has widespread applications in statistics and machine learning. The method choice is, however, difficult due to the abundance of proposed methods and the lack of neutral comparison studies,…