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We address the question whether the sequence of areas between coalescing random walkers displays multiscaling and in the process calculate the second moment as well as the two point correlation function exactly. The scaling of higher order…
The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
One of the firm predictions of inflationary cosmology is the consistency relation between scalar and tensor spectra. It has been argued that such a relation -if experimentally confirmed- would offer strong support for the idea of inflation.…
We develop notions of integrable functions within the theory of schemic motivic integration.
A distribution function approach is applied to describe the dynamics of the laser beam in the Earth atmosphere. Using a formal solution of the kinetic equation for the distribution function, we have developed an iterative scheme for…
Passing from a microscopic discrete lattice system with many degrees of freedom to a mesoscopic continuum system described by a few coarse-grained equations is challenging. The common folklore is to take the thermodynamic limit so that the…
A fluctuation relation for aging systems is introduced, and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase space regions in a scenario of entropy-driven relaxation. The…
We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton…
We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a…
Within recently proposed scenario which explains flatness of the spectrum of scalar cosmological perturbations by a combination of conformal and global symmetries, we discuss the effect of weak breaking of conformal invariance. We find that…
We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
We revisit the problem of inelastic times governing the temperature behavior of the weak localization correction and mesoscopic fluctuations in one- and two-dimensional systems. It is shown that, for dephasing by the electron electron…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
We present accurate predictions of the correlation function of hotspots in the microwave background radiation for gaussian theories such as those predicted in most inflation models. The correlation function of peaks above a certain…
While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find…
Using a single-scattering theory, we derive the expression of the degree of polarization of the light scattered from a layer exhibiting both surface and volume scattering. The expression puts forward the intimate connection between the…