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The well-known Isothermal Theorem was introduced in a Nature Communications article in 2005 and has since contributed to the creation of the rich field of evolutionary graph theory. The theorem states under which conditions certain…
We continue the study of partition functions of 5d supersymmetric theories on manifolds taking the form of a twisted product $\mathcal{M}_3\times \Sigma_{\mathfrak{g}}$ with $\Sigma_{\mathfrak{g}}$ denoting a Riemann surface of genus…
It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…
We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
The characteristic predictions of chiral soliton models - the Skyrme model and its extentions - are discussed. The chiral soliton models prediction of dibaryon states with masses below NN-pion threshold is in qualitative agreement with…
An alternative generating function is proposed to enumerate row-convex polyominoes without internal holes on a discrete grid. The approach is based on integer partitions of the total area, where each partition corresponds to a sequence of…
We develop the study of a particular class of biorthogonal measures, encompassing at the same time several random matrix models and partition functions of polymers. This general framework allows us to characterize the partition functions of…
For each $n\geq 1$, we express the partition function $p(n)$ as a CM trace on $X_0(6)$ of the discriminant $\Delta_n:=1-24n$ invariants of a weight 0 weak Maass function $P$ that records where CM elliptic curves sit on $X(1)$, together with…
Each of the local isometry groups arising in 3d gravity can be viewed as the group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement, and use it as a…
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights…
Several natural complex configuration spaces admit surprising uniformizations as arithmetic ball quotients, by identifying each parametrized object with the periods of some auxiliary object. In each case, the theory of canonical models of…
We study the dimer model for a planar bipartite graph N embedded in a disk, with boundary vertices on the boundary of the disk. Counting dimer configurations with specified boundary conditions gives a point in the totally nonnegative…
A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We prove results that suggest surprising usefulness for such a…
We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized $J_3 \bar J_3$ deformed $AdS_3$ with periodic Euclidean time as an integral transform of the partition function of the undeformed Euclideanized…
A mathematical model of the distribution function for the discrete 3-disk is proposed in order to utilize in the statistical evolution equation of the 3-dimensional Universe. The model distribution is constructed based on analyses in known…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
Dirac fermions have a central role in high energy physics but it is well known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the…
We present analytic models for the local structure of self-regulated self-gravit ating accretion discs that are subject to realistic cooling. Such an approach can be used to predict the secular evolution of self-gravitating discs (which can…