Related papers: Critical point correlations in random gaussian fie…
We prove convergence of the full extremal process of the two-dimensional scale-inhomogeneous discrete Gaussian free field in the weak correlation regime. The scale-inhomogeneous discrete Gaussian free field is obtained from the 2d discrete…
The universal conductance fluctuations of quasi-two-dimensional systems are analyzed with experimental considerations in mind. The traditional statistical metrics of these fluctuations (such as variance) are shown to have large statistical…
We proposed a new universal method for significantly increasing accuracy of critical points of 2 and 3-dimensional Ising models and exploring fluctuation mechanism. The method is based on analysis of block fractals and the renormalization…
We study the landscape complexity of the Hamiltonian $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a smooth Gaussian process with isotropic increments on $\mathbb R^{N}$. This model describes a single particle on a random potential in…
Padmanabhan (1996) has suggested a model to relate the nonlinear two - point correlation function to the linear two - point correlation function. In this paper, we extend this model in two directions: (1) By averaging over the initial…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the $d$-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair…
Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as…
An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation…
We introduce a novel unbiased, cross-correlation estimator for the one-point statistics of cosmological random fields. One-point statistics are a useful tool for analysis of highly non-Gaussian density fields, while cross-correlations…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
We study asymptotic expansions of spin-spin correlation functions for the XXZ Heisenberg chain in the critical regime. We use the fact that the long-distance effects can be described by the Gaussian conformal field theory. Comparing exact…
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension $\xt$. We consider the case when the boundary…
We consider the initial energy density in the transverse plane of a high energy nucleus-nucleus collision as a random field $\rho(\x)$, whose probability distribution $P[\rho]$, the only ingredient of the present description, encodes all…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…
The thermodynamic limit of the dynamical density and spin-density two-point correlation functions for the spin Calogero-Sutherland model are derived from Uglov's finite-size results. The resultant formula for the density two-point…
Using a quadratic saddle-point approximation, we show how information about a particle-emitting source can be extracted from gaussian fits to two-particle correlation data. Although the formalism is completely general, extraction of the…
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential…
We investigate the distribution of critical points of certain isotropic random functions $\Phi$ on $\mathbb{R}^m$. We show that the distribution of critical points of $\Phi(Rx)$, suitably normalized, converge a.s. and $L^2$ as random…