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We study mesoscopic linear statistics for a class of determinantal point processes which interpolates between Poisson and Gaussian Unitary Ensemble statistics. These processes are obtained by modifying the spectrum of the correlation kernel…
We study a 2-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S.Kerov, G.Olshanski and A.Vershik, Comptes Rendus…
We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with Gaussian initial condition. In particular, we examine the validity and limitations of one-point…
We investigate the clustering of halos in cosmological models starting with general local-type non-Gaussian primordial fluctuations. We employ multiple Gaussian fields and add local-type non-Gaussian corrections at arbitrary order to cover…
We implement a novel formalism to constrain primordial non-Gaussianity of the local type from the large-scale modulation of the small-scale power spectrum. Our approach combines information about primordial non-Gaussianity contained in the…
The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function…
Starting from first principles, we derive the fundamental equations that relate the $n$-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full…
We study non-Gaussianities in the primordial perturbations in single field inflation where there is radiation era prior to inflation. Inflation takes place when the energy density of radiation drops below the value of the potential of a…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
We investigate properties of the correlation function of clusters of galaxies using geometrical models. On small scales the correlation function depends on the shape and the size of superclusters. On large scales it describes the geometry…
We revisit the derivation of the mass function and the bias of dark matter halos for non-Gaussian initial conditions. We use a steepest-descent approach to point out that exact results can be obtained for the high-mass tail of the halo mass…
Employing the perturbative treatment of gravitational clustering, we discuss possible effects of primordial non-Gaussianity on the matter power spectrum. As gravitational clustering develops, the coupling between different Fourier modes of…
The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to…
Threshold biasing of a Gaussian random field gives a linear amplification of the reduced two point correlation function at large distances. We show that for standard cosmological models this does not translate into a linear amplification of…
We compute the angular two-point correlation functions of the gamma-ray bursts at cosmological distances. Since the gamma-ray burst emission mechanism is not yet established, we simply assume that the gamma-ray burst sources are associated…
The higher order moments of the fluctuations for the thermodynamical systems in the presence of fields are investigated in the framework of a theoretical method. The metod uses a generalized statistical ensemble consonant with the adequate…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
We present a coarse-grained field theory of density fluctuations for a Newtonian self-gravitating many-body system and apply it to a homogeneous Universe with small density fluctuations. The theory treats the clustering of galaxies and…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
We derive analytically the spatial correlation functions for gap fluctuations in two-band scenario with intra- and interband pair-transfer interactions. These functions demonstrate the changes in spatial functionality due to the presence of…