710 research outputs found
Pseudoconvex regions of finite D'Angelo type in four dimensional almost complex manifolds
Let D be a J-pseudoconvex region in a smooth almost complex manifold (M,J) of
real dimension four. We construct a local peak J-plurisubharmonic function at
every boundary point p of finite D'Angelo type. As applications we give local
estimates of the Kobayashi pseudometric, implying the local Kobayashi
hyperbolicity of D at p. In case the point p is of D'Angelo type less than or
equal to four, or the approach is nontangential, we provide sharp estimates of
the Kobayashi pseudometric.Comment: 34 page
Almost complex structures on the cotangent bundle
We construct some lift of an almost complex structure to the cotangent
bundle, using a connection on the base manifold. This generalizes the complete
lift defined by I.Sato and the horizontal lift introduced by K.Yano and
S.Ishihara. We study some geometric properties of this lift and its
compatibility with symplectic forms on the cotangent bundle.Comment: 14 page
Fluctuations of the Empirical Measure of Freezing Markov Chains
In this work, we consider a finite-state inhomogeneous-time Markov chain
whose probabilities of transition from one state to another tend to decrease
over time. This can be seen as a cooling of the dynamics of an underlying
Markov chain. We are interested in the long time behavior of the empirical
measure of this freezing Markov chain. Some recent papers provide almost sure
convergence and convergence in distribution in the case of the freezing speed
, with different limits depending on or
. Using stochastic approximation techniques, we generalize these
results for any freezing speed, and we obtain a better characterization of the
limit distribution as well as rates of convergence as well as functional
convergence.Comment: 30 page
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