10,406 research outputs found
Power-law behavior and condensation phenomena in disordered urn models
We investigate equilibrium statistical properties of urn models with
disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and
the other corresponds to the Monkey class. These models are introduced from the
view point of the power-law behavior and randomness; it is clarified that
quenched random parameters play an important role in generating power-law
behavior. We evaluate the occupation probability with which an urn has
balls by using the concept of statistical physics of disordered systems. In
the disordered urn model belonging to the Monkey class, we find that above
critical density for a given temperature, condensation
phenomenon occurs and the occupation probability changes its scaling behavior
from an exponential-law to a heavy tailed power-law in large regime. We
also discuss an interpretation of our results for explaining of macro-economy,
in particular, emergence of wealth differentials.Comment: 16pages, 9figures, using iopart.cls, 2 new figures were adde
Collective behavior of stock prices as a precursor to market crash
We study precursors to the global market crash that occurred on all main
stock exchanges throughout the world in October 2008 about three weeks after
the bankruptcy of Lehman Brothers Holdings Inc. on 15 September. We examine the
collective behavior of stock returns and analyze the market mode, which is a
market-wide collective mode, with constituent issues of the FTSE 100 index
listed on the London Stock Exchange. Before the market crash, a sharp rise in a
measure of the collective behavior was observed. It was shown to be associated
with news including the words "financial crisis." They did not impact stock
prices severely alone, but they exacerbated the pessimistic mood that prevailed
among stock market participants. Such news increased after the Lehman shock
preceding the market crash. The variance increased along with the cumulative
amount of news according to a power law.Comment: 10 pages, 7 figure
Invariant subspaces with no generator and a problem of H. Helson
In the almost periodic context, any space cannot be generated by one
of its elements. Together with cocycle argument, this derives that there exist
all kinds of invariant subspaces without single generator, from which we can
answer some questions on invariant subspace theory.Comment: 19 page
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