Related papers: Summing all the eikonal graphs. II
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a…
Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…
Ferromagnetic models are harmonic oscillators in statistical mechanics. Beyond their original scope in tackling phase transition and symmetry breaking in theoretical physics, they are nowadays experiencing a renewal applicative interest as…
We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…
The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in…
With the present paper we conclude the presentation of a semianalytical model of hierarchical clustering of bound virialized objects formed by gravitational instability from a random Gaussian field of density fluctuations. In paper I, we…
Systems with many interacting stochastic constituents are fully characterized by their free energy. Computing this quantity is therefore the objective of various approaches, notably perturbative expansions, which are applied in problems…
The (disjoint) fort number and fractional zero forcing number are introduced and related to existing parameters including the (standard) zero forcing number. The fort hypergraph is introduced and hypergraph results on transversals and…
The eikonal approximation is at the heart of many theoretical and phenomenological studies involving multiple soft gauge boson emissions in high energy physics. We describe our efforts towards the extension of the eikonal approximation for…
The feasibility conditions obtained in a previous report are refined, and used to determine several infinite families of feasible parameters for strongly regular graphs with no triangles. The methods are also used to improve the lower bound…
A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a…
We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at…
We establish a lower bound for the energy of a complex unit gain graph in terms of the matching number of its underlying graph, and characterize all the complex unit gain graphs whose energy reaches this bound.
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
We present a new expression of the scattering amplitude, valid for spherical absorbing objects, which leads to an improved version of the eikonal method outside the diffraction region. Limitations of this method are discussed and numerical…
While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by…
Following recent studies of Ford, we suggest -- in the framework of general relativity -- an inflationary cosmological model with the self-interacting spinning matter. A generalization of the standard fluid model is discussed and estimates…