Related papers: Large deviation principles for words drawn from co…

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the \emph{annealed} large deviation principle (LDP) for the empirical process of words, the rate…

Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…

We derive an annealed large deviation principle (LDP) for the normalised and rescaled local times of a continuous-time random walk among random conductances (RWRC) in a time-dependent, growing box in $\Z^d$. We work in the interesting case…

We prove the analogue for continuous space-time of the quenched LDP derived in Birkner, Greven and den Hollander (2010) for discrete space-time. In particular, we consider a random environment given by Brownian increments, cut into pieces…

We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of…

Consider the inhomogeneous Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices for which each pair $i,j\in\{1,\ldots,n\}$, $i\neq j$ is connected independently by an edge with probability $r_n(\frac{i-1}{n},\frac{j-1}{n})$, where…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

We consider a dynamic Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices in which each edge switches on at rate $\lambda$ and switches off at rate $\mu$, independently of other edges. The focus is on the analysis of the evolution of the…

We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures…

We derive properties of the rate function in Varadhan's (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zero set of the rate function. Our approach…

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…

Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a Large Deviation Principle (LDP) for these random graphs, viewed as elements of…

We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…

Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…

Letting~$N=\left\{N(t), t\geq0\right\}$ be a standard Poisson process, Stroock~ \cite{Stroock-1981} constructed a family of continuous processes by $$\Theta_{\epsilon}(t)=\int_0^t\theta_{\epsilon}(r)dr, \ \ \ \ \ 0 \le t \le 1,$$ where…

Establishing a Large Deviation Principle (LDP) proves to be a powerful result for a vast number of stochastic models in many application areas of probability theory. The key object of an LDP is the large deviations rate function, from which…

We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random perturbation. First, we demonstrate the existence and uniqueness…

A uniform key renewal theorem is deduced from the uniform Blackwell's renewal theorem. A uniform LDP (large deviations principle) for renewal-reward processes is obtained, and MDP (moderate deviations principle) is deduced under conditions…

Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path evolution of the empirical degree distribution…