Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200

Global validity of the Master kinetic equation for hard-sphere systems

Following the recent establishment of an exact kinetic theory realized by the Master kinetic equation which describes the statistical behavior of the Boltzmann-Sinai Classical Dynamical System (CDS), in this paper the problem is posed of the construction of the related global existence and regularity theorems. For this purpose, based on the global prescription of the same CDS for arbitrary single- and multiplecollision events, first global existence is extablished for the N-body Liouville equation which is written in Lagrangian differential and integral forms. This permits to reach the proof of global existence both of generic N-body probability density functions (PDF) as well as of particular solutions which maximize the statistical Boltzmann-Shannon entropy and are factorized in terms of the corresponding 1-body PDF. The latter PDF is shown to be uniquely defined and to satisfy the Master kinetic equation globally in the extended 1-body phase space. Implications concerning the global validity of the asymptotic Boltzmann equation and Boltzmann H-theorem are discussed

Applying a markov chain model in quality function deployment

Markov chain model, Quality function deployment, Technical measure, House of quality, Transition matrix,