18,094 research outputs found
Mayer expansion of the Nekrasov pre potential: the subleading -order
The Mayer cluster expansion technique is applied to the Nekrasov instanton
partition function of super Yang-Mills. The
subleading small -correction to the Nekrasov-Shatashvili limiting
value of the prepotential is determined by a detailed analysis of all the
one-loop diagrams. Indeed, several types of contributions can be distinguished
according to their origin: long range interaction or potential expansion,
clusters self-energy, internal structure, one-loop cyclic diagrams, etc.. The
field theory result derived more efficiently in [1], under some minor technical
assumptions, receives here definite confirmation thanks to several remarkable
cancellations: in this way, we may infer the validity of these assumptions for
further computations in the field theoretical approach.Comment: 29 pages, 9 figure
Correlation, hierarchies, and networks in financial markets
We discuss some methods to quantitatively investigate the properties of
correlation matrices. Correlation matrices play an important role in portfolio
optimization and in several other quantitative descriptions of asset price
dynamics in financial markets. Specifically, we discuss how to define and
obtain hierarchical trees, correlation based trees and networks from a
correlation matrix. The hierarchical clustering and other procedures performed
on the correlation matrix to detect statistically reliable aspects of the
correlation matrix are seen as filtering procedures of the correlation matrix.
We also discuss a method to associate a hierarchically nested factor model to a
hierarchical tree obtained from a correlation matrix. The information retained
in filtering procedures and its stability with respect to statistical
fluctuations is quantified by using the Kullback-Leibler distance.Comment: 37 pages, 9 figures, 3 table
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