4,179 research outputs found
Simultaneous nonparametric inference of time series
We consider kernel estimation of marginal densities and regression functions
of stationary processes. It is shown that for a wide class of time series, with
proper centering and scaling, the maximum deviations of kernel density and
regression estimates are asymptotically Gumbel. Our results substantially
generalize earlier ones which were obtained under independence or beta mixing
assumptions. The asymptotic results can be applied to assess patterns of
marginal densities or regression functions via the construction of simultaneous
confidence bands for which one can perform goodness-of-fit tests. As an
application, we construct simultaneous confidence bands for drift and
volatility functions in a dynamic short-term rate model for the U.S. Treasury
yield curve rates data.Comment: Published in at http://dx.doi.org/10.1214/09-AOS789 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Innermost stable circular orbits of charged spinning test particles
The effects of a paritcle's spin and electric charge on its angular momentum,
energy and radius on the innermost stable circular orbit are investigated based
on the particle's equations of motion in a background of the Kerr-Newmann
spacetime. It is found that the particle's angular momentum and energy have
monotonous relationships with not only its spin but also its charge; it is also
discovered that the spinning particle's radius may change non-monotonously with
its charge. Hence, our result remarkably indicates that particles owning
identical spin but different charge may degenerate into a same last stable
circular orbit.Comment: 6 page
Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly
We investigate the phase transitions of black holes with conformal anomaly in
canonical ensemble from different perspectives. Some interesting and novel
phase transition phenomena have been discovered. Firstly, we discuss the
behavior of the specific heat and the inverse of the isothermal
compressibility. It is shown that there are striking differences in Hawking
temperature and phase structure between black holes with conformal anomaly and
those without it. In the case with conformal anomaly, there exists local
minimum temperature corresponding to the phase transition point. Phase
transitions take place not only from an unstable large black hole to a locally
stable medium black hole but also from an unstable medium black hole to a
locally stable small black hole. Secondly, we probe in details the dependence
of phase transitions on the choice of parameters. The results show that black
holes with conformal anomaly have much richer phase structure than those
without it. There would be two, only one or no phase transition points
depending on the parameters we have chosen. The corresponding parameter region
are derived both numerically and graphically. Thirdly, geometrothermodynamics
are built up to examine the phase structure we have discovered. It is shown
that Legendre invariant thermodynamic scalar curvature diverges exactly where
the specific heat diverges. Furthermore, critical behaviors are investigated by
calculating the relevant critical exponents. It is proved that these critical
exponents satisfy the thermodynamic scaling laws, leading to the conclusion
that critical exponents and the scaling laws can reserve even when we consider
conformal anomaly.Comment: some new references adde
Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble
Recently, extended phase space thermodynamics of Lovelock AdS black holes has
been of great interest. To provide insight from a different perspective and
gain a unified phase transition picture, non-extended phase space
thermodynamics of -dimensional charged topological Lovelock AdS black
holes is investigated detailedly in the grand canonical ensemble. Specifically,
the specific heat at constant electric potential is calculated and phase
transition in the grand canonical ensemble is discussed. To probe the impact of
the various parameters, we utilize the control variate method and solve the
phase transition condition equation numerically for the case . There
are two critical points for the case while there is only one for
other cases. For , there exists no phase transition point. To figure out
the nature of phase transition in the grand canonical ensemble, we carry out an
analytic check of the analog form of Ehrenfest equations proposed by Banerjee
et al. It is shown that Lovelock AdS black holes in the grand canonical
ensemble undergo a second order phase transition. To examine the phase
structure in the grand canonical ensemble, we utilize the thermodynamic
geometry method and calculate both the Weinhold metric and Ruppeiner metric. It
is shown that for both analytic and graphical results that the divergence
structure of the Ruppeiner scalar curvature coincides with that of the specific
heat. Our research provides one more example that Ruppeiner metric serves as a
wonderful tool to probe the phase structures of black holes
P-V criticality of conformal anomaly corrected AdS black holes
The effects of conformal anomaly on the thermodynamics of black holes are
investigated in this Letter from the perspective of criticality of AdS
black holes. Treating the cosmological constant as thermodynamic pressure, we
extend the recent research to the extended phase space. Firstly, we study the
- criticality of the uncharged AdS black holes with conformal anomaly and
find that conformal anomaly does not influence whether there exists Van der
Waals like critical behavior. Secondly, we investigate the - criticality
of the charged cases and find that conformal anomaly influences not only the
critical physical quantities but also the ratio . The ratio
is no longer a constant as before but a function of conformal anomaly parameter
. We also show that the conformal parameter should satisfy a
certain range to guarantee the existence of critical point that has physical
meaning. Our results show the effects of conformal anomaly
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