Related papers: Finite-$N$ Bootstrap Constraints in Matrix and Ten…
$O(N)$ invariant vector models have been shown to possess non-trivial scaling large $N$ limits, at least perturbatively within the loop expansion, a property they share with matrix models of 2D quantum gravity. In contrast with matrix…
The quadratic minimum spanning tree problem and its variations such as the quadratic bottleneck spanning tree problem, the minimum spanning tree problem with conflict pair constraints, and the bottleneck spanning tree problem with conflict…
We consider the problem of quantization of the bosonic membrane via the large $N$ limit of its matrix regularizations $H_N$ in Fock space. We prove that there exists a choice of the Fock space frequency such that $ H_N$ can be written as a…
This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. These equations are parameterized by a degree n polynomial W_n(x), and the general solution is labeled by an arbitrary function of…
We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
We revisit the space of gapped quantum field theories with a global O(N) symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories such as the non-linear sigma model…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…
The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming…
Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…
In this work, we derive novel constraints on scalar-tensor theories from neutrino physics. Spatial variations of the background scalar field effectively generate density and position-dependent Standard Model masses, including neutrinos.…
Many physical systems like supersymmetric Yang-Mills theories are formulated as quantum matrix models. We discuss how to apply the Beth ansatz to exactly solve some supersymmetric quantum matrix models in the large-N limit. Toy models are…
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…
The bootstrap programme for finding exact S-matrices of integrable quantum field theories with N=1 supersymmetry is investigated. New solutions are found which have the same fusing data as bosonic theories related to the classical affine…