Random Tensor models: Combinatorics, Geometry, Quantum Gravity and Integrability
Abstract
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 introduction to few aspects of random matrix models and recalling a physical motivation called Group Field Theory, we start exploring the world of random tensor models and its relation to geometry, quantum gravity and combinatorics. We first define these models in a natural way and discuss their geometry and combinatorics. After these first explorations we start generalizing random matrix methods to random tensors in order to describes the mathematical and physical properties of random tensor models, at least in some specific cases.
Cite
@article{arxiv.1512.01472,
title = {Random Tensor models: Combinatorics, Geometry, Quantum Gravity and Integrability},
author = {Stephane Dartois},
journal= {arXiv preprint arXiv:1512.01472},
year = {2015}
}
Comments
PhD Manuscript, 163 pages, based on several precedent results. Contains some unpublished results. Summary and Acknowledgments in French. Main body of the manuscript in English