Related papers: Large Deviations of Telecom Processes

We consider the point process of signal strengths emitted from transmitters in a wireless network and observed at a fixed position. In our model, transmitters are placed deterministically or randomly according to a hard core or Poisson…

In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

The contact process and the slightly different susceptible-infected-susceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and…

The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their…

We consider directed acyclic networks with multiple sources and multiple terminals where each source generates one i.i.d. random process over an abelian group and all the terminals want to recover the sum of these random processes. The…

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…

We consider the point process of signal strengths from transmitters in a wireless network observed from a fixed position under models with general signal path loss and random propagation effects. We show via coupling arguments that under…

Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…

In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov…

If you take a superposition of n IID copies of a point process and thin that by a factor of 1/n, then the resulting process tends to a Poisson point process as n tends to infinity. We give a simple proof of this result that highlights its…

Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…

Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…

To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating…

Functional limit theorems are presented for the rescaled occupation time fluctuations process of a critical finite variance branching particle system in $R^d$ with symmetric a-stable motion starting off from either a standard Poisson random…

This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…