Related papers: Random Matrices, Boundaries and Branes

We present a class of solvable models that resemble string theories in many respects but have a strikingly different non-perturbative sector. In particular, there are no exponentially small contributions to perturbation theory in the string…

This article provides a self contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being…

Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…

We investigate the local spectral statistics of the loss surface Hessians of artificial neural networks, where we discover excellent agreement with Gaussian Orthogonal Ensemble statistics across several network architectures and datasets.…

We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…

We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel…

We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…

We introduce a new parametrisation for the Fermi sea of the $c = 1$ matrix model. This leads to a simple derivation of the scattering matrix, and a calculation of boundary corrections in the corresponding $1+1$--dimensional string theory.…

The solution of constrained linear partial-differential equations can be described via parametric representations of linear relations. To study these representations, we provide a novel definition of boundary triplets for linear relations…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…

Using the construction of D-branes with nonzero $B$ field in the matrix model we give a physical interpretation of the known background independence in gauge theories on a noncommutative space. The background independent variables are…

We investigate the recently developed theory of multiple membranes. In particular, we consider open membranes, i.e. the theory defined on a membrane world volume with a boundary. We first restrict our attention to the gauge sector of the…

I present a new formalism of the R-matrix theory where the formal parameters for the resonance energies and widths are identical to the observed values. By allowing the boundary condition parameters to vary from level to level, the freedom…

We study branes and open strings in a large class of orbifolds of a curved background using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex…

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution…

We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of…

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…

We develop further a new geometrical model of a discretized string, proposed in [1] and establish its basic physical properties. The model can be considered as the natural extention of the usual Feynman amplitude of the random walks to…

Spectrum of elementary string states in type II string theory contains ultra-short multiplets that are marginally stable. $U$-duality transformation converts these states into bound states at threshold of $p$-branes carrying Ramond-Ramond…