Related papers: Punctures and p-spin curves from matrix models II
What is the connection of random matrices with integrable systems? Is this connection really useful? Introducing apprpriate times in the distribution of the ensemble of matrices, one shows that the corresponding distribution of the…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new…
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
Let $p$ be a prime number, and let $\Delta_1,\Delta_2 < 0$ be two coprime fundamental discriminants. When $p$ splits in $\mathbb{Q}(\sqrt{\Delta_1})$ and $\mathbb{Q}(\sqrt{\Delta_2})$ the height pairings of the corresponding CM divisors on…
Modular curves like X_0(N) and X_1(N) appear very frequently in arithmetic geometry. While their complex points are obtained as a quotient of the upper half plane by some subgroups of SL_2(Z), they allow for a more arithmetic description as…
We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
Nonperturbative corrections in type II string theory corresponding to Riemann surfaces with one boundary are calculated in several noncompact geometries of desingularized orbifolds. One of these models has a complicated phase structure…
We introduce the notion of crossings and nestings of a permutation. We compute the generating function of permutations with a fixed number of weak exceedances, crossings and nestings. We link alignments and permutation patterns to these…
The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory…
The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
Multivariate circular observations, i.e. points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this…
In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full…
The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidrv; the limiting rescaled spectral measure (LRSM)…
We discover that tautological intersection numbers on $\bar{\mathcal{M}}_{g, n}$, the moduli space of stable genus $g$ curves with $n$ marked points, are evaluations of Ehrhart polynomials of partial polytopal complexes. In order to prove…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We study the supersingular curves on Picard modular surfaces modulo a prime $p$ which is inert in the underlying quadratic imaginary field. We analyze the automorphic vector bundles in characteristic $p$, and as an application derive a…