1,025 research outputs found
On a class of distributions stable under random summation
We investigate a family of distributions having a property of
stability-under-addition, provided that the number of added-up random
variables in the random sum is also a random variable. We call the
corresponding property a \,-stability and investigate the situation with
the semigroup generated by the generating function of is commutative.
Using results from the theory of iterations of analytic functions, we show that
the characteristic function of such a -stable distribution can be
represented in terms of Chebyshev polynomials, and for the case of -normal
distribution, the resulting characteristic function corresponds to the
hyperbolic secant distribution. We discuss some specific properties of the
class and present particular examples.Comment: 12 pages, 1 figur
Absorption by Threebranes and the AdS/CFT Correspondence
In the first part of this talk I discuss two somewhat different supergravity
approaches to calculating correlation functions in strongly coupled Yang-Mills
theory. The older approach relates two-point functions to cross-sections for
absorption of certain incident quanta by threebranes. In this approach the
normalization of operators corresponding to the incident particles is fixed
unambiguously by the D3-brane DBI action. By calculating absorption
cross-sections of all partial waves of the dilaton we find corresponding
two-point functions at strong `t Hooft coupling and show that they are
identical to the weak coupling results. The newer approach to correlation
functions relates them to boundary conditions in AdS space. Using this method
we show that for a certain range of negative mass-squared there are two
possible operator dimensions corresponding to a given scalar field in AdS, and
indicate how to calculate correlation functions for either of these choices. In
the second part of the talk I discuss an example of AdS/CFT duality which
arises in the context of type 0 string theory. The CFT on N coincident electric
and magnetic D3-branes is argued to be stable for sufficiently weak `t Hooft
coupling. It is suggested that its transition to instability at a critical
coupling is related to singularity of planar diagrams.Comment: 14 pages, LaTeX; Talk at Strings '99, Potsdam, German
Heavy-tailed probability distributions in social sciences
We present an overview of possible reasons for the appearance of heavy-tailed
distributions in applications to the natural sciences. These distributions
include the laws of Pareto, Lotka, and some new ones. The reasons are
illustrated using suitable toy models.
Keywords: heavy-tailed distributions; Pareto law; Lotka law; Zipf law;
probability generating function
Cycle of the needs satisfaction, and information support of the society development simulation system
The report focuses on some of the key points of constructing a model of an artificial society. It is based on the processes of emergence and implementation of the needs of specific agents, depending on the internal processes in the agents, and external environmental factors. Unlike in other approaches, the basis of the modeled system agents' behavior is the concept of needs as the necessity of implementation of the agents' transition from one state to another. This article presents an algorithm of the needs satisfaction of the agent, starting with the event that caused the need for, and ending its satisfaction, or the message that it is impossible to satisfy. The basis of objective knowledge in the system are a model of active and passive agents, as well as recipes meet the needs of the active agents and the relationships between them. © 2017 Author(s)
Fuzzy spaces and new random matrix ensembles
We analyze the expectation value of observables in a scalar theory on the
fuzzy two sphere, represented as a generalized hermitian matrix model. We
calculate explicitly the form of the expectation values in the large-N limit
and demonstrate that, for any single kind of field (matrix), the distribution
of its eigenvalues is still a Wigner semicircle but with a renormalized radius.
For observables involving more than one type of matrix we obtain a new
distribution corresponding to correlated Wigner semicircles.Comment: 12 pages, 1 figure; version to appear in Phys. Rev.
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