Related papers: Maximal height statistics for 1/f^alpha signals
We study the distribution and scaling of the extreme height fluctuations for Edwards-Wilkinson-type relaxation on small-world substrates. When random links are added to a one-dimensional lattice, the average size of the fluctuations becomes…
In this paper we present the distribution of the maximum of the telegraph process in the cases where the initial velocity is positive or negative with an even and an odd number of velocity reversals. For the telegraph process with positive…
We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on $\mathbb{R}^{\Lambda_N}$, $\Lambda_N=[-N, N]^d\cap \mathbb{Z}^d$ with Hamiltonian $H_N(\phi)=…
We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
The $\alpha$-$\eta$-$\kappa$-$\mu$ is one of the most generalized and flexible channel models having an excellent fit to experimental data from diverse propagation environments. The existing statistical results on the envelope of…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…
The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer…
We prove for the rescaled convolution map $f\to f\circledast f$ propagation of polynomial, exponential and gaussian localization. The gaussian localization is then used to prove an optimal bound on the rate of entropy production by this…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
This paper studies a scalar Gaussian wiretap channel where instead of an average input power constraint, we consider a peak amplitude constraint on the input. The goal is to obtain insights into the secrecy-capacity and the structure of the…
We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…
In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
We study numerically the maximal and minimal height distributions (MAHD, MIHD) of the nonlinear interface growth equations of second and fourth order and of related lattice models in two dimensions. MAHD and MIHD are different due to the…