Related papers: Sample path large deviations for queueing networks…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
We consider the Minimum Description Length principle for online sequence prediction. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is…
In this paper we show the distributions of sliding block patterns for Bernoulli processes with finite alphabet, which is not based on the induction on sample size. We show a new inclusion-exclusion formula in multivariate generating…
We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation…
We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of…
Understanding human mobility is of vital importance for urban planning, epidemiology, and many other fields that aim to draw policies from the activities of humans in space. Despite recent availability of large scale data sets related to…
The Join-the-Shortest-Queue routing policy is studied in an asymptotic regime where the number of processors $n$ scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as $n\to \infty$, in…
Inference and prediction are fundamental to the study of complex systems, where network data are often incomplete, inaccurate or obtained indirectly. In this paper, we review recent advances in network sampling and comparison, as well as in…
Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
We consider a model of queues in discrete time, with batch services and arrivals. The case where arrival and service batches both have Bernoulli distributions corresponds to a discrete-time M/M/1 queue, and the case where both have…
This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under…
We show quenched large deviations for the simple random walk on a certain class of percolations with long-range correlations. This class contains the supercritical Bernoulli percolations, the model considered by Drewitz, R'ath and…
In this work, we propose a novel probabilistic sequence model that excels at capturing high variability in time series data, both across sequences and within an individual sequence. Our method uses temporal latent variables to capture…
We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the…
We prove a large deviation principle for the finite dimensional marginals of the Gibbs distribution of the macroscopic `overlap'-parameters in the Hopfield model in the case where the number of random patterns, $M$, as a function of the…
Network traffic data is huge, varying and imbalanced because various classes are not equally distributed. Machine learning (ML) algorithms for traffic analysis uses the samples from this data to recommend the actions to be taken by the…
This paper studies the network throughput and transport delay of a multihop wireless random access network based on a Markov renewal model of packet transportation. We show that the distribution of the source-to-destination (SD) distance…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…
This note describes several open questions concerning scaling limits of queue-length processes of symmetric queues in heavy traffic, distinguishing between service-time distributions with finite and infinite variance.