Related papers: Supersymmetric Matrix Models and the Meander Probl…
Some results in random matrices are generalized to supermatrices, in particular supermatrix integration is reduced to an integration over the eigenvalues and the resulting volume element is shown to be equivalent to a one dimensional…
A family of random models for bosonic quasi-particle excitations, e.g. the vibrations of a disordered solid, is introduced. The generator of the linearized phase space dynamics of these models is the sum of a deterministic and a random…
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
I review some recent works on the Hermitean one-matrix and d-dimensional gauge-invariant matrix models. Special attention is paid to solving the models at large-N by the loop equations. For the one-matrix model the main result concerns…
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
It has been argued that the bosonic large-$N$ master field of the IIB matrix model can give rise to an emergent classical spacetime. In a recent paper, we have obtained solutions of a simplified bosonic master-field equation from a related…
By extending the algebraic description of the bosonic rank-three tensor models, a general framework for super rank-three tensor models and correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy spaces must satisfy a…
We present a supersymmetric model in which the observed fermion masses and mixings are generated by localizing the three generations of matter and the two Higgs fields at different locations in a compact extra dimension. Supersymmetry is…
We reexamine the external field problem for $N\times N$ hermitian one-matrix models. We prove an equivalence of the models with the potentials $\tr{({1/over2N}X^2 + \log X - \Lambda X)}$ and $\sum_{k=1}^\infty t_k\tr{X^k}$ providing the…
We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
We explain the motivation and main ideas underlying our proposal for a Lagrangian for Matrix Theory based on sixteen supercharges. Starting with the pedagogical example of a bosonic matrix theory we describe the appearance of a continuum…
In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model {\it via}…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
The problem of counting polymer coverings on the rectangular lattices is investigated. In this model, a linear rigid polymer covers $k$ adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites…
Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The…
In the monomer-polymer model, a linear rigid polymer covers $k$ adjacent lattice sites, with no lattice site occupied by more than one polymer. The polymers are called $k$-mers, and those unoccupied lattice sites are called monomers. The…
We discuss the matrix model in a class of 11D time dependent supersymmetric backgrounds as obtained in hep-th/0508191 . We construct the matrix model action through the matrix regularization of the membrane action in the background. We show…