Related papers: Summing all the eikonal graphs. II
In applications, quantities of interest are often modelled in equilibrium or an equilibrium solution is sought. The presence of confounding makes causal inference in this setting challenging. We provide interpretable graphical models for…
We show how to obtain rising hadronic total cross sections in QCD, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlators. Total cross sections turn out to be of "Froissart"-type,…
Quantifying the flow of energy within and through fluctuating nanoscale systems poses a significant challenge to understanding microscopic biological machines. A common approach involves coarse-graining, which allows a simplified…
We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its…
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs…
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates…
In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get cancelled in the sum. This is known to happen in large-$N_c$ QCD in the presence of a baryon, and also in the case of…
In the theoretical analysis of high-energy elastic nucleon scattering one starts commonly from the description based on the validity of optical theorem, which allows to derive the value of total cross section directly from the…
A remarkably simple dependence of fragmentation cross-section on average binding energy has been established in experimental data. This dependence was empirically parametrised leading to a very useful formula for extrapolation. We find that…
Start with a graph with a subset of vertices called {\it the border}. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaos Solitons & Fractals, 139,110003 (2020)]. We determine the conditions for having fat-tailed…
Observations of the cosmic microwave sky are revealing the primordial non-uniformities from which all structure in the Universe grew. The only known physical mechanism for generating the inhomogeneities we see involves the amplification of…
A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian)…
We have investigated the detailed structure of $l$-plane singularities of scattering amplitude saturating the Froissart bound. A self-consistent analysis of these singularities provides us secondary terms in the Froissart bound. These…
We study the energy per vertex in regular graphs. For every k, we give an upper bound for the energy per vertex of a k-regular graph, and show that a graph attains the upper bound if and only if it is the disjoint union of incidence graphs…
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…
A model where the inflationary phase emerges as a response to protect the Fischler-Susskind holographic bound is described. A two fluid model in a closed universe inflation picture is assumed, and a discussion on conditions under which is…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
Game comonads have brought forth a new approach to studying finite model theory categorically. By representing model comparison games semantically as comonads, they allow important logical and combinatorial properties to be exressed in…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…