Related papers: Randomness in infinitesimal extent in the McLerran…
We consider the nodal length $L(\lambda)$ of the restriction to a ball of radius $r_\lambda$ of a {\it Gaussian pullback monochromatic random wave} of parameter $\lambda>0$ associated with a Riemann surface $(\mathcal M,g)$ without…
We improve the McLerran-Venugopalan model by introducing a charge-density correlation function which is consistent with the observation that nucleons carry no net color charge. The infrared divergence in the transverse coordinates that was…
We study random walk among random conductance (RWRC) on complete graphs with N vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution…
In this paper, we consider $m$ independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the $m$ rectangular matrices is an $n$ by…
Nonstandard analysis and electromagnetic propagation properties are used to derive all of the fundamental results for the Special Theory of Relativity. Infinitesimal modeling via infinitesimal light-clocks is used to derive two general…
The Johnson-Lindenstrauss Lemma states that there exist linear maps that project a set of points of a vector space into a space of much lower dimension such that the Euclidean distance between these points is approximately preserved. This…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
We make precise sense of the idea of "molecular chaos" through algorithmic randomness of microscopic trajectories, and ground macroscopic irreversibility in the lack of symmetry under time reversal of this property. This concept of…
We study the impact of finite-size effect on continuous variable source-independent quantum random number generation. The central-limit theorem and maximum likelihood estimation theorem are used to derive the formula which could output the…
This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…
We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution…
We modify the McLerran-Venugopalan model to include only a finite number of sources of color charge. We argue that Coulombic interactions between these color charges generates a source-source correlation function that properly includes the…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
For a regression model, we consider the risk of the maximum likelihood estimator with respect to $\alpha$-divergence, which includes the special cases of Kullback-Leibler divergence, Hellinger distance and $\chi^2$ divergence. The…
Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…
The celebrated invariance property states that particles entering a bounded domain, with isotropic and uniform incidence, spend on average $\langle \ell \rangle=4V/S$ length inside, no matter how they scatter. We show that this remarkable…
We present our progress on simulating the Glasma in the early stages of heavy ion collisions in a non-boost-invariant setting. Our approach allows us to describe colliding nuclei with finite longitudinal width by extending the…