Harmonicity of Gibbs Measures
نویسنده
چکیده
In this paper we extend the construction of random walks with a prescribed Poisson boundary found in [CM04] to the case of measures in the class of a generalized Gibbs state. The price for dropping the α-quasiconformal assumptions is that we must restrict our attention to CAT(−κ) groups. Apart from the new estimates required, we prove a new approximation scheme to provide a positive basis for positive functions in a metric measure space.
منابع مشابه
New harmonicity measures for pitch estimation and voice activity detection
Harmonic structure can be easily recognized in the timefrequency representation of speech signals even in the diverse environment. The harmonicity is a measure of the completeness of harmonic structure. This paper extends the use of conventional harmonicity measure to the tasks of pitch estimation and voice activity detection. A set of hierarchical harmonicities, including grid, temporal, spect...
متن کاملHarmonicity and Minimality of Vector Fields on Lorentzian Lie Groups
We consider four-dimensional lie groups equipped with left-invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields defining harmonic maps, and calculate explicitly the energy of t...
متن کاملMusical Consonance: The Importance of Harmonicity
A recent study suggests that musical consonance is based on harmonicity, a preference that reflects the central role of harmonicity in auditory perception.
متن کاملVariational Principle for Fuzzy Gibbs Measures
In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memoryless channels in information theory, continuous block factors of sym...
متن کاملClassical Limits of Euclidean Gibbs States for Quantum Lattice Models
Models of quantum and classical particles on the d–dimensional lattice ZZ with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the particle m = μ/h̄ tends to infinity. For these models, it is proposed to define the convergence of the Euclidean Gibbs states, when m → +∞, by the weak convergence of...
متن کامل