Related papers: Big Numbers in String Theory
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
A new semianalytical model that explains the formation and sizes of the 'great walls' - the largest structures observed in the universe is suggested. Although the basis of the model is the Zel'dovich approximation it has been used in a new…
On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the…
We study the structure of the non-perturbative free energy of a one-parameter class of little string theories (LSTs) of A-type in the so-called unrefined limit. These theories are engineered by $N$ M5-branes probing a transverse flat space.…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
An analytic model of long string network evolution, recently developed by the authors, is presented in detail, and modified to describe string loop evolution. By treating the average string velocity, as well as the characteristic…
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…
We describe how the strings, which are classical solutions of the continuum three-dimensional U(1)+Higgs theory, can be studied on the lattice. The effect of an external magnetic field is also discussed and the first results on the string…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
I discuss the usefulness of lattice supersymmetry in relation to string phenomenology. I suggest how lattice results might be incorporated into string phenomenology. I outline difficulties and describe some constructions that contain an…
The string number of self-maps arose in the context of algebraic entropy and it can be viewed as a kind of combinatorial entropy function. Later on its values for endomorphisms of abelian groups were calculated in full generality. We study…
Free probability theory started in the 1980s has attracted much attention lately in signal processing and communications areas due to its applications in large size random matrices. However, it involves with massive mathematical concepts…
A personal view is given of the development of string theory out of dual models, including the analysis of the structure of the physical states and the proof of the No-Ghost Theorem, the quantization of the relativistic string, and the…
We construct an addition and a multiplication on the set of planar binary trees, closely related to addition and multiplication on the integers. This gives rise to a new kind of (noncommutative) arithmetic theory. The price to pay for this…
Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…
H.Furstenberg and E.Glasner proved that for an arbitrary $k\in\mathbb{N}$, any piecewise syndetic set of integers contains a $k$-term arithmetic progression and the collection of such progressions is itself piecewise syndetic in…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…