Related papers: Random vector and matrix and vector theories: a re…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
We show that if the non Gaussian part of the cumulants of a random matrix model obey some scaling bounds in the size of the matrix, then Wigner's semicircle law holds. This result is derived using the replica technique and an analogue of…
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this…
The density matrix renormalization group is applied to a relativistic complex scalar field at finite chemical potential. The two-point function and various bulk quantities are studied. It is seen that bulk quantities do not change with the…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…
The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
The functional renormalisation group for the Einstein-Hilbert action is investigated for the case of four infinite (or large) and one compact dimension. The motivation for this study is given by the suggestion that gravity in more than four…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
We consider the scattering matrices of massive quantum field theories with no bound states and a global $O(N)$ symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass $m$…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…
The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
A first step in the analysis of the renormalizability of gravity at Large N is carried on. Suitable resummations of planar diagrams give rise to a theory in which there is only a finite number of primitive superficially divergent Feynman…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann…