Related papers: Random systems and replica field theory
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
This is an introduction to some of the most probabilistic aspects of free probability theory.
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
We derive randomization-based models for experiments with a chain of randomizations. The estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the…
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…
We present some aspects of the rheology of field-responsive suspensions, a class of field-responsive liquid matter systems possessing the ability to undergo significant changes in their strength upon application of an external field. Both…
The fluctuations in the particle size distribution for processes of fragmentation and aggregation are studied for stationary state regimes. The system is described in terms of a stochastic process over an adequate tree structure. The RMS…
1 - Introduction 2 - Small-Angle Bhabha Scattering and the Luminosity Measurement 3 - Z^0 Physics 4 - Fits to Precision Data 5 - Physics at LEP2 6 - Conclusions
This lecture has the following sections: Systems and States; Brownian Motion; Segmental Relaxation and the Glass Transition; Dynamics of a Free Chain; Entanglement and Reptation. Appendices cover: Linear response theory, relaxation,…
Contents: 1.- Introduction 2.- Scaling of entanglement in (1+1)-dimensional systems 3.- Entanglement and RG-flows 4.- Matrix Product States Appendix A.- Entanglement and order relations B.- Hilbert space in a conformal theory
In this paper, the foundations of classical phenomenological thermodynamics are being thoroughly revisited. A new rigorous basis for thermodynamics is laid out in the main text and presented in full detail in the appendix. All relevant…
In this report I discuss fluctuation theorems and transient violations of the second law of thermodynamics in small systems. Special emphasis is placed on free-energy recovery methods in the framework of non-equilibrium single-molecule…
Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…
With the help of mathematical technique of irreducible tensors the multipole expansion for the probability amplitude of spontaneous radiation of a quantum system is derived. It is shown that the found series represents the total radiation…
An electromagnetic theory of thermal radiation is outlined, based on the fluctuation electrodynamics of Rytov and co-workers. We discuss the basic concepts and the status of different approximations. The physical content is illustrated with…
It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are…
We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.
Using theoretical and numerical arguments we discuss some of the commonly accepted approximations for the radiative transfer equations in climatology.