83,587 research outputs found
Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces
We develop a Thermodynamic Formalism for bounded continuous potentials
defined on the sequence space , where is a general
Borel standard space. In particular, we introduce meaningful concepts of
entropy and pressure for shifts acting on and obtain the existence of
equilibrium states as additive probability measures for any bounded continuous
potential. Furthermore, we establish convexity and other structural properties
of the set of equilibrium states, prove a version of the
Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity
of the potential and show that the Yosida-Hewitt decomposition of these
equilibrium states do not have a purely additive part.
We then apply our results to the construction of invariant measures of
time-homogeneous Markov chains taking values on a general Borel standard space
and obtain exponential asymptotic stability for a class of Markov operators. We
also construct conformal measures for an infinite collection of interacting
random paths which are associated to a potential depending on infinitely many
coordinates. Under an additional differentiability hypothesis, we show how this
process is related after a proper scaling limit to a certain infinite
dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical
Systems. 23 page
Interpolation of bilinear operators and compactness
The behavior of bilinear operators acting on interpolation of Banach spaces
for the method in relation to the compactness is analyzed. Similar
results of Lions-Peetre, Hayakawa and Person's compactness theorems are
obtained for the bilinear case and the method.Comment: This work was published at "Nonlinear Analysis: Theory, Methods and
Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some
gaps in the original proof of Theorem 4.3, Here we give a new proof. For
this, we change the Lemma 4.
Effective action for a quantum scalar field in warped spaces
We investigate the one-loop corrections at zero, as well as finite
temperature, of a scalar field taking place in a braneworld motived warped
background. After to reach a well defined problem, we calculate the effective
action with the corresponding quantum corrections to each case.Comment: 10 pages, to appear in The European Physical Journal
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