595 research outputs found
Nonergodicity and Central Limit Behavior for Long-range Hamiltonians
We present a molecular dynamics test of the Central Limit Theorem (CLT) in a
paradigmatic long-range-interacting many-body classical Hamiltonian system, the
HMF model. We calculate sums of velocities at equidistant times along
deterministic trajectories for different sizes and energy densities. We show
that, when the system is in a chaotic regime (specifically, at thermal
equilibrium), ergodicity is essentially verified, and the Pdfs of the sums
appear to be Gaussians, consistently with the standard CLT. When the system is,
instead, only weakly chaotic (specifically, along longstanding metastable
Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time
averages) is observed, and robust -Gaussian attractors emerge, consistently
with recently proved generalizations of the CLT.Comment: 6 pages 7 figures. Improved version accepted for publication on
Europhysics Letter
Perfect Information vs Random Investigation: Safety Guidelines for a Consumer in the Jungle of Product Differentiation
We present a graph-theoretic model of consumer choice, where final decisions
are shown to be influenced by information and knowledge, in the form of
individual awareness, discriminating ability, and perception of market
structure. Building upon the distance-based Hotelling's differentiation idea,
we describe the behavioral experience of several prototypes of consumers, who
walk a hypothetical cognitive path in an attempt to maximize their
satisfaction. Our simulations show that even consumers endowed with a small
amount of information and knowledge may reach a very high level of utility. On
the other hand, complete ignorance negatively affects the whole consumption
process. In addition, rather unexpectedly, a random walk on the graph reveals
to be a winning strategy, below a minimal threshold of information and
knowledge.Comment: 27 pages, 12 figure
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