Related papers: Probability distribution over some phenomenologica…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…
Reasoning about the pose, i.e. position and orientation of objects is one of the cornerstones of robotic manipulation under uncertainty. In a number of joint research projects our group is developing a robotic perception system that…
Given a matrix $A\in \mathrm{GL}_d(\mathbb{Z})$. We study the pseudorandomness of vectors $\mathbf{u}_n$ generated by a linear recurrent relation of the form $$ \mathbf{u}_{n+1} \equiv A \mathbf{u}_n \pmod {p^t}, \qquad n = 0, 1, \ldots, $$…
Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that each f^i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
We discuss the compactification of type I strings on a torus with additional background gauge flux on the D9-branes. The solutions to the cancellation of the RR tadpoles display various phenomenologically attractive features: supersymmetry…
We analyze the tree-level potential of type IIB flux compactifications in warped Calabi-Yau orientifolds, in regions of weak coupling and moderately large complex structure. In this regime, one may approximate the flux-induced…
This paper introduces two families of probability distributions for Bayesian analysis of hypertoroidal data. The first family consists of symmetric distributions derived from the projection of multivariate normal distributions under…
We construct a set of chirality inducing G_4-fluxes in global F-theory compactifications on Calabi-Yau four-folds. Special emphasis is put on models with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model building,…
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…
Matter and pressure distribution in hadrons are studied in a dual analytic model of generalized parton distributions with complex Regge trajectories. An original parametrization for pressure distribution in the nucleon is proposed ensuring…
We develop tools for analyzing the space of intersecting brane models. We apply these tools to a particular T^6/Z_2^2 orientifold which has been used for model building. We prove that there are a finite number of intersecting brane models…
We study novel type IIB compactifications on the T^6/Z_2 orientifold. This geometry arises in the T-dual description of Type I theory on T^6, and one normally introduces 16 space-filling D3-branes to cancel the RR tadpoles. Here, we cancel…
Pattern formation in a two-dimensional system of rod-like particles has been simulated using a lattice approach. Rod-like particles were modelled as linear $k$-mers of two mutually perpendicular orientations ($k_x$- and $k_y$-mers) on a…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…
We consider a certain convolution semigroup $\Theta$ of probability distributions on the group $\mathbb{R}\times \mathbb{Z}(2)$, where $\mathbb{R}$ is the group of real numbers and $\mathbb{Z}(2)$ is the additive group of the integers…
In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of…
We propose a minimal SO(10) model in 5 space-time dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam. The breaking down to the standard model group…
Many datasets are observed on a finite set of equally spaced directions instead of the exact angles, such as the wind direction data. However, in the statistical literature, bivariate models are only available for continuous circular random…