Related papers: Russo's formula for random interlacements
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
The random intensity of noise approach to 1D Laval-Dubrulle-Nazarenko model is used to describe Lagrangian acceleration of a fluid particle in developed turbulence. Intensities of noises entering nonlinear Langevin equation are assumed to…
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y…
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
The paper formulates the concept of persistence of excitation for discrete-time linear switched systems, and provides sufficient conditions for an input signal to be persistently exciting. Persistence of excitation is formulated as a…
We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with…
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
We consider the goal of predicting how complex networks respond to chronic (press) perturbations when characterizations of their network topology and interaction strengths are associated with uncertainty. Our primary result is the…
Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…
The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…
This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse…
In earlier work the authors obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here formulas are obtained for joint probabilities for several particles. In the case of a single…
Extending the classical Dirichlet's density theorem on coprime pairs, in this paper we describe completely the probability distribution of the number of coprime pairs in random squares of fixed side length in the lattice $\mathbb{N}^2$. The…
We prove a generalized version of Rogers' mean value formula in the space $X_n$ of unimodular lattices in $R^n$, which gives the mean value of a multiple sum over a lattice $L$ and its dual $L^*$. As an application, we prove that for $L$…