arXiv subjects

Senya Shlosman

Publications and source records attributed to Senya Shlosman.

47 records · Page 3Linked to original sources

arXiv2007

Dobrushin Interfaces via Reflection Positivity

We study the interfaces separating different phases of 3D systems by means of the Reflection Positivity method. We treat discrete non-linear sigma-models, which exhibit power-law decay of correlations at low temperatures, and we prove the rigidity property of the interface. Our method is applicable to the Ising and Potts models, where it simplifies the derivation of some known results. The method also works for large-entropy systems of continuous spins.

math-ph↗

arXiv2005

Self-averaging property of queuing systems

We establish the averaging property for a queuing process with one server, M(t)/GI/1. It is a new relation between the output flow rate and the input flow rate, crucial in the study of the Poisson Hypothesis. Its implications include the statement that the output flow always possesses more regularity than the input flow.

math.PR↗

arXiv2004

Poisson Hypothesis for Information Networks II. Cases of Violations and Phase Transitions

We present examples of queuing networks that never come to equilibrium. That is achieved by constructing Non-linear Markov Processes, which are non-ergodic, and possess eternal transience property.

math-ph↗

arXiv2004

3D crystal: how flat its flat facets are?

We investigate the hypothesis that the (random) crystal of the $(-)$-phase inside the $(+)$-phase of the 3D canonical Ising model has flat facets. We argue that it might need to be weakened, due to the possibility of formation of extra monolayer on a facet. We then prove this weaker hypothesis for the Solid-On-Solid model.

math-ph↗

arXiv2003

Magnetostriction Transition

We present a non mean-field model which undergoes a magnetostriction phase transition in the temperature. That is, the crystal becomes sharply contracted and magnetized once the temperature passes below the critical value

math-ph↗

arXiv2003

Poisson Hypothesis for information networks (A study in non-linear Markov processes)

In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov processes, have a line of fixed points which are global attractors. To do this we derive the corresponding non-linear integral equation and we explore its self-averaging properties. Our derivation relies on a solution of a combinatorial problem of rode placements.

math-ph↗

arXiv2001

2D models of statistical physics with continuous symmetry: the case of singular interactions

We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular interactions with continuous symmetry, when the symmetry is broken in the thermodynamic limit.

math.PR↗

arXiv2001

Applications of the Wulff construction to the number theory

We apply the geometric construction of solutions of some variational problems of combinatorics to estimate the number of partitions and of plane partitions of an integer.

math-ph↗

arXiv2000

Random Lattices and Random Sphere Packings: Typical Properties

We review results about the density of typical lattices in $R^n.$ They state that such density is of the order of $2^{-n}.$ We then obtain similar results for random packings in $R^n$: after taking suitably a fraction $ν$ of a typical random packing $σ$, the resulting packing $τ$ has density $C(ν) 2^{-n},$ with a reasonable $C(ν).$ We obtain estimates on $C(ν).$

math-ph↗

arXiv2000

Wulff construction in statistical mechanics and in combinatorics

We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.

math-ph↗

arXiv2000

Geometric variational problems of statistical mechanics and of combinatorics

We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.

math-ph↗