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We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $\tau$ between volume volatilities above a given threshold q. For different…
The relation between the results of cosmological N-body simulations, and the continuum theoretical models they simulate, is currently not understood in a way which allows a quantification of N dependent effects. In this first of a series of…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
For a probability distribution $P$ on an at most countable alphabet $\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\mathbb E K_{n,r}$ and probabilities $\mathbb E M_{n,r}$. Both upper and lower…
Naive estimates of the statistics of large scale structure and weak lensing power spectrum measurements that include only Gaussian errors exaggerate their scientific impact. Non-linear evolution and finite volume effects are both…
We show how to obtain the probability density function for the amplitude of the curvature perturbation, R, produced during an epoch of slow-roll, single-field inflation, working directly from n-point correlation functions of R. These…
The effects of discreteness arising from the use of the N-body method on the accuracy of simulations of cosmological structure formation are not currently well understood. After a discussion of how the relevant discretisation parameters…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
We investigate the possible accuracy that can be reached by analytical models for the matter density power spectrum and correlation function. Using a realistic description of the power spectrum that combines perturbation theory with a halo…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
We study the probability distribution $P$ of the sum of a large number of non-identically distributed random variables $n_m$. Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk…
Spontaneous collapse models aim to solve the long-standing measurement problem in quantum mechanics by modifying the theory's dynamics to include objective wave function collapses. These collapses occur randomly in space, bridging the gap…
We compute analytically the probability distribution function ${\cal P}(\epsilon)$ of the dissipation field $\epsilon =(\nabla \theta)^{2}$ of a passive scalar $\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet…
We discuss probability distributions for the cosmological constant Lambda and the amplitude of primordial density fluctuations Q in models where they both are anthropic variables. With mild assumptions about the prior probabilities, the…
The theory of influences in product measures has profound applications in theoretical computer science, combinatorics, and discrete probability. This deep theory is intimately connected to functional inequalities and to the Fourier analysis…
We calculate the one-point probability distribution function (PDF) for cosmic density in non-linear regime of the gravitational evolution. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the…
We study the statistics of a system of N random levels with integer values, in the presence of a logarithmic repulsive potential of Dyson type. This probleme arises in sums over representations (Young tableaux) of GL(N) in various matrix…