Related papers: Logarithmic variance for the height function of sq…
We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim 1/k$, where $k$ is the wave number. From very-high-resolution numerical simulations, in the…
We prove an analog of Schmid's $\text{\rm SL}_2$-orbit theorem for a class of variations of mixed Hodge structure which includes logarithmic deformations, degenerations of 1-motives and archimedean heights. In particular, as consequence…
In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near…
We study the limiting behavior of random lozenge tilings of the hexagon with a q-Racah weight as the size of the hexagon grows large. Based on the asymptotic behavior of the recurrence coefficients of the q-Racah polynomials, we give a new…
In this paper, we got some refinements of the norm inequalities related to the Heinz mean and logarithmic mean.
We investigate the surface width $W$ of solid-on-solid surfaces in the vicinity of the roughening temperature $T_r$. Above $T_r$, $W^2$ is expected to diverge with the system size $L$ like $\ln L$. However, close to $T_r$ a clean $\ln{L}$…
The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which…
The free energy of a two-dimensional system at criticality has in general an universal part proportional the logarithm of the system size. This term was shown by Cardy and Peschel to be related to the curvature of the system, with smooth…
For a cycle of codimension 1 in a toric variety, its degree with respect to a nef toric divisor can be understood in terms of the mixed volume of the polytopes associated to the divisor and to the cycle. We prove here that an analogous…
The variations of Hodge structures of weight one associated to square-tiled surfaces naturally generate interesting subgroups of integral symplectic matrices called Kontsevich--Zorich monodromies. In this paper, we show that arithmetic…
We define a lattice model for the interaction of a polymer with water. We solve the model in a suitable approximation. In the case of a non-polar homopolymer, for reasonable values of the parameters, the polymer is found in a non-compact…
Given a square-free monomial ideal $I$ in a polynomial ring $R$ over a field $\mathbb{K}$, one can associate it with its LCM-lattice and its hypergraph. In this short note, we establish the connection between the LCM-lattice and the…
We study perfect matchings on the square-hexagon lattice with $1\times n$ periodic edge weights such that the boundary condition is given by either (1) each remaining vertex on the bottom boundary is followed by $(m-1)$ removed vertices;…
Hwang in [Phys. Rev. E 80, 042103 (2009)] suggested that the two transitions of the six-state clock model on the square lattice are not of the Kosterlitz-Thouless type. Here we show from simulations thatat the upper transition, the helicity…
In a recent work by Cruz-Uribe et al. was obtained that \[|\{x\in{\mathbb{R}^d}:w(x)|G(fw^{-1})(x)|>\alpha\}|\lesssim\frac{[w]_{A_1}^2}{\alpha}\int_{{\mathbb{R}^d}}|f|dx\] both in the matrix and scalar settings, where $G$ is either the…
We present a detailed probabilistic and structural analysis of the set of weighted homomorphisms from the discrete torus $\mathbb{Z}_m^n$, where $m$ is even, to any fixed graph: we show that the corresponding probability distribution on…
The salinity of water and the slope of ice significantly influence the melt rate and surface morphology of ice, both highly relevant in the context of glacier and iceberg melting in oceanic environments. In this study, we conducted…
Interfacial phenomena associated with fluid adsorption in two dimensional systems has recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We…
We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of…
Let F be a function field of one variable over an algebraically closed field of characteristic zero, X a geometrically irreducible smooth projective variety over F, and L a line bundle on X. In this note, we will prove that if the…