Related papers: Large deviations for a damped telegraph process
We consider a continuous time Markov chain on a countable state space. We prove a joint large deviation principle (LDP) of the empirical measure and current in the limit of large time interval. The proof is based on results on the joint…
This paper focuses on the consensus averaging problem on graphs under general noisy channels. We study a particular class of distributed consensus algorithms based on damped updates, and using the ordinary differential equation method, we…
Behind the nice unification provided by the notion of the level 2.5 in the field of large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between the meaning of the…
We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the…
We consider an irreducible continuous time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for…
This paper presents an empirical study of the relationship between the density of small-medium sized random graphs and their planarity. It is well known that, when the number of vertices tends to infinite, there is a sharp transition…
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…
This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail,…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
We formulate large deviations principle (LDP) for diffusion pair $(X^\epsilon,\xi^\epsilon)=(X_t^\epsilon,\xi_t^\epsilon)$, where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time.…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
The objective of this article is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size tends to infinity. Here, a random cubical filtration is an increasing family of random…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Diffusion state distance (DSD) is a metric on the vertices of a graph, motivated by bioinformatic modeling. Previous results on the convergence of DSD to a limiting metric relied on the definition being based on symmetric or reversible…
Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…
We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be…
The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval $(0,s)$ by working on the…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…