Related papers: Matrix Models, Quantum Penner Action and Two-Dimen…
The ten dimensional heterotic string effective action with graviton, dilaton and antisymmetric tensor fields is dimensionally reduced to two spacetime dimensions. The resulting theory, with some constraints on backgrounds, admits infinite…
Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
It is generally accepted that the double-scaled 1D matrix model is equivalent to the $c=1$ string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest…
Starting from $W_{\infty}$ as a fundamental symmetry and using the coadjoint orbit method, we derive an action for one dimensional strings. It is shown that on the simplest nontrivial orbit this gives the single scalar collective field…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We consider a spin-s Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path…
We study the hermitian one matrix model with semi-classical potential. This is a general unitary invariant random matrix ensemble in which the potential has a derivative that is a rational function and the measure is supported on some…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
We analyze when an arbitrary matrix pencil is equivalent to a dissipative Hamiltonian pencil and show that this heavily restricts the spectral properties. In order to relax the spectral properties, we introduce matrix pencils with…
We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle eigenfunctions of the entanglement…
Matrix models have wide applications in nuclear theory, condensed matter theory and quantum field theory. I discuss supersymmetric extensions of matrix models and their applications to branched polymers, the meander problem, and…
We derive a concrete closed string dual to any interacting Hermitian one-matrix model, away from the double-scaling limit. Matrix and string correlators manifestly agree, to all orders in the genus expansion and all orders in the 't Hooft…
We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics…
This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states…
We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where…
We find the precise relationship between the loop gas method and the matrix quantum mechanics approach to two-dimensional string theory. The two systems are distinguished by different target spaces ($\Z$ and $\R$, respectively) as far as…
The k-point correlation functions of the Gaussian Random Matrix Ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We…
We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…