相关论文: Dimers and Amoebae

We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…

We consider two different versions of the double dimer model on a planar domain, where we either fold a single dimer cover on a symmetric domain onto itself across the line of symmetry, or we superimpose two independent dimer covers on two,…

We consider random n-covers $X_n$ of an arbitrary compact hyperbolic surface $X$. We show that in the large n regime and small window limit, the variance of the smooth spectral statistics of the Laplacian twisted by a unitary abelian…

In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying the power spectrum of the surface and its relation to the…

We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…

Ellerman bombs (EBs) seem to be a part of a whole spectrum of phenomena that might have the same underlying physical mechanism, but with observed characteristics which pose a considerable challenge to models. The aim of this study is to…

For surface-mediated processes, such as on-surface synthesis, epitaxial growth and heterogeneous catalysis, a constant slope in the Arrhenius diagram of the corresponding rate of interest against inverse temperature, $\log R$ {\it vs}…

In 2003, van Dam and Haemers posed a fundamental question in spectral graph theory: does there exist a ``sensible'' matrix whose spectrum determines a random graph up to isomorphism? This paper introduces the class of {\em natural graph…

We discuss spontaneously broken quantum field theories with a continuous symmetry group via the constraint effective potential. Employing lattice simulations with constrained values of the order parameter, we demonstrate explicitly that the…

We consider a uniform spanning tree in a $\delta$-square grid approximation of a planar domain $\Omega$. For given integer $n\ge 2$, we condition the tree on the following $n$-arm event: we pick $n$ branches, emanating from $n$ points…

There is a natural link between (multi-)curves that fill up a closed oriented surface and dessins d'enfants. We use this approach to exhibit explicitly the minima of the geodesic length function of a kind of curves (uniform filling curves)…

Auto- and cross-spectral density functions for dynamic {random} fields and power are derived. These are based on first- and second-order Pad\'{e} approximants of correlation functions expanded in terms of spectral moments. The second-order…

Let $G$ be a bipartite planar graph with edges directed from black to white. For each vertex $v$ let $n_v$ be a positive integer. A multiweb in $G$ is a multigraph with multiplicity $n_v$ at vertex $v$. A connection is a choice of linear…

We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of…

We investigate the spectral distribution of the damped wave equation on a compact Riemannian manifold, especially in the case of a metric of negative curvature, for which the geodesic flow is Anosov. The main application is to obtain…

For the case of algebraic curves - compact Riemann surfaces - it is shown that de Rham cohomology group $H^{1}_{\mathrm{dR}}(X,\mathbb{C})$ of a genus $g$ Riemann surface $X$ has a natural structure of a symplectic vector space. Every…

We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…

The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock…

The spectral properties of disordered fully-connected graphs with a special type of the node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on…

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…