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All species of (non-conformally-coupled) particles are produced during inflation so long as their mass $M$ is not too much larger than $H$, the expansion rate during inflation. It has been shown that if a particle species that is normally…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The impact of particle production during inflation on the primordial curvature perturbation spectrum is investigated both analytically and numerically. We obtain an oscillatory behavior on small scales, while on large scales the spectrum is…
We study cosmological evolution after inflation in models with non-minimal derivative coupling to gravity. The background dynamics is solved and particle production associated with rapidly oscillating Hubble parameter is studied in detail.…
Higher-curvature corrections to the effective gravitational action may leave signatures in the spectrum of primordial tensor perturbations if the inflationary energy scale is sufficiently high. In this paper we further investigate the…
The Epps effect is key phenomenology relating to high frequency correlation dynamics in financial markets. We argue that it can be used to provide insight into whether tick data is best represented as samples from Brownian diffusions, or as…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the…
We present a collection of tools automating the efficient computation of large sets of theory predictions for high-energy physics. Calculating predictions for different processes often require dedicated programs. These programs, however,…
We discuss particle production mechanisms for heavy ion collisions. We present an argument demonstrating how the fluctuations of the number of produced particles in a series of classical emissions can account for KNO scaling. We predict…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon…
We study extremal correlation functions of chiral primary operators in the large-N SU(N) ${\cal N} = 2$ superconformal QCD theory and present new results based on supersymmetric localization. We discuss extensively the basis-independent…
The new three year WMAP data seem to confirm the presence of non-standard large scale features in the Cosmic Microwave Anisotropies power spectrum. While these features may hint at uncorrected experimental systematics, it is also possible…
We continue the study of the correlation functions for the point stochastic processes introduced in Part I (G.Olshanski, math.RT/9804086). We find an integral representation of all the correlation functions and their explicit expression in…
Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an n-th order exceptional point, n eigenvalues and the corresponding…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
The statistical analysis of marked point processes requires disentangling complex spatial arrangements from attribute-dependent interactions. While classical summary statistics are effective for second-order dependencies, they frequently…
Recent results from the Atacama Cosmology Telescope (ACT), when combined with Planck and DESI datasets, indicate a scalar spectral index $n_s$ larger than that reported in the Planck 2018 baseline, thereby challenging conventional…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…