Related papers: The OSSS Method in Percolation Theory
We study random coloring of the hexagons of a honeycomb lattice into $2^{n-1}$ colors (that is the standard Potts model at infinite temperature). It may be considered as a generalization of percolation to $n$ pairwise independent, but…
Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing…
Over the past 36 years much research has been carried out on Bessel beams (BBs) owing to their peculiar properties, viz non-diffraction behavior, self-healing nature, possession of well-defined orbital angular momentum with helical…
Expanding upon previous work, using the path-integral formalism we derive expressions for the one-particle reduced density matrix and the two-point correlation function for a quadratic system of bosons that interact through a general class…
The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional…
Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through…
Boson sampling is the task of producing samples from the number-basis distribution of many bosons traveling through a passive linear optical network. It is believed to be extremely difficult to accomplish classically, and has been the…
We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point…
Distillation has shown remarkable success in transferring knowledge from a Large Language Model (LLM) teacher to a student LLM. However, current distillation methods require similar tokenizers between the teacher and the student,…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
The properties of 3D Bose-Einstein condensate have been studied with variational and numerical methods. In the variational approach, we use the super-Gaussian trial function, and it is demonstrated that this trial function gives a good…
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…
We present a theoretical study of transport properties of a liquid comprised of particles uist1:/home/sokrates/egorov/oldhome/Pap41/Submit > m abs.tex We present a theoretical study of transport properties of a liquid comprised of particles…
We introduce a cohomology theory that classifies differential objects that arise from Picard-Vessiot theory, using the differential Hopf-Galois descent. To do this, we provide an explicit description of Picard-Vessiot theory in terms of…
In this work, we numerically study the higher-ordered/extended Boussinesq system describing the propagation of water-waves over flat topography. A reformulation of the same order of precision that avoids the calculation of high order…
Percolation phenomena are investigated and discussed in three kinds of nanostructures: first two are nanocrystalline silicon-based systems, Si nanodots embedded in amorphous SiO2 matrix and porous silicon formed by an oxidized nanowire…
Recently, Rissanen et al., (2022) have presented a new type of diffusion process for generative modeling based on heat dissipation, or blurring, as an alternative to isotropic Gaussian diffusion. Here, we show that blurring can equivalently…
Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…
This is a new book of quantum Hierarchic theory of condensed matter, general for liquids and solids, developed by this author during 20 years and its numerous applications. Computer program, based on new theory, was used for simulations of…
This work presents a theoretical model of boson sampling with optical feedback, in which a subset of the interferometer's output modes is looped back into the input modes. If the bosons are injected periodically into the input modes of the…