Zobrazeno 1 - 10
of 162
pro vyhledávání: '"Suhov, Y."'
The purpose of this note is to consider a number of straightforward generalizations of the Pirogov-Sinai theory which can be covered by minor additions to the canonical texts. These generalizations are well-known among the adepts of the Pirogov-Sinai
Externí odkaz:
http://arxiv.org/abs/2409.02328
We study the hard-core model of statistical mechanics on a unit cubic lattice $\mathbb{Z}^3$, which is intrinsically related to the sphere-packing problem for spheres with centers in $\mathbb{Z}^3$. The model is defined by the sphere diameter $D>0$ w
Externí odkaz:
http://arxiv.org/abs/2304.08642
We present a new self-contained proof of the well-known fact that the minimal area of a Voronoi cell in a unit circle packing is equal to $2\sqrt{3}$, and the minimum is achieved only on a perfect hexagon. The proof is short and, in our opinion, inst
Externí odkaz:
http://arxiv.org/abs/2211.03255
We perform a rigorous study of the identical sphere packing problem in $\mathbb{Z}^3$ and of phase transitions in the corresponding hard-core model. The sphere diameter $D>0$ and the fugacity $u\gg 1$ are the varying parameters of the model. We solve
Externí odkaz:
http://arxiv.org/abs/2112.14250
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically linearly wi
Externí odkaz:
http://arxiv.org/abs/2112.05877
We study dense packings of disks and related Gibbs distributions representing high-density phases in the hard-core model on unit triangular, honeycomb and square lattices. The model is characterized by a Euclidean exclusion distance $D>0$ and a value
Externí odkaz:
http://arxiv.org/abs/2011.14156
This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic for the prob
Externí odkaz:
http://arxiv.org/abs/1911.03981
We study the Gibbs statistics of high-density hard-core configurations on a unit square lattice $\mathbb{Z}^2$, for a general Euclidean exclusion distance $D$. As a by-product, we solve the disk-packing problem on $\mathbb{Z}^2$ for disks of diameter
Externí odkaz:
http://arxiv.org/abs/1909.11648
The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled process cont
Externí odkaz:
http://arxiv.org/abs/1806.08956
We perform a rigorous study of the Gibbs statistics of high-density hard-core random configurations on a unit triangular lattice $\mathbb{A}_2$ and a unit honeycomb graph $\mathbb{H}_2$, for any value of the (Euclidean) repulsion diameter $D>0$. Only
Externí odkaz:
http://arxiv.org/abs/1803.04041