Related papers: Random systems and replica field theory
This is a submission to the Encyclopedia of Mathematical Physics (Elsevier, 2006) and conforms to its referencing guidelines.
This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.
We review the paper [arXiv:1905.12783] and discuss some comments about SYK on random unicycle.
I briefly describe two motivations, two mechanisms and two possible tests of the hypothesis that the physical parameters of the ground state of a theory can vary in different regions of the universe.
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to…
Kinematical and dynamical properties of chaotic systems are reviewed and a few applications are described.
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This is a draft version of Part II of a three-part textbook on quantum field theory.
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…
Contents: 1 Frustrated quantum spin systems 1.1 The Pyrochlore checkerboard 1.2 Singlets in reflection symmetric spin systems 2 Wehrl entropy of Bloch coherent states 2.1 Conjectures of Wehrl and Lieb 2.2 Proof of Lieb's conjecture for low…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the…
Diffusion-encoded magnetic resonance (MR) experiments can provide important insights into the microstructural characteristics of a variety of biological tissues and other fluid- or gas-filled porous media. The physics of diffusion encoding…
The real- and imaginary-time-formalisms of thermal field theory and their extension to gauge theories is reviewed. Questions of gauge (in-)dependence are discussed in detail, in particular the possible gauge dependences of the singularities…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…