Stationary distributions for a class of generalized Fleming-Viot processes

We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration.Comment: Published in at http://dx.doi.org/10.1214/12-AOP829 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entanglement branching operator

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.Comment: 11 pages, 13 figure

Distances and lensing in cosmological void models

We study the distances and gravitational lensing in spherically symmetric inhomogeneous cosmological models consisting of inner and outer homogeneous regions which are connected by a single shell or double shells at the redshift $z_1 \sim 0.067$. The density and Hubble parameters in the inner region are assumed to be smaller and larger, respectively, than those in the outer region. It is found that at the stage $z_1 < z < 1.5$ the distances from an observer in the inner void-like region are larger than the counterparts (with equal $z$) in the corresponding homogeneous Friedmann models, and hence the magnitudes for the sources at this stage are larger. This effect of the void-like low-density region may explain the deviations of the observed [magnitude-redshift] relation of SNIa from the relation in homogeneous models, independently of the cosmological constant. When the position of the observer deviates from the center, moreover, it is shown that the distances are anisotropic and the images of remote sources are systematically deformed. The above relation at $z \geq 1.0$ and this anisotropy will observationally distinguish the role of the above void-like region from that of the positive cosmological constant. The influence on the time-delay measurement is also discussed.Comment: 14 pages, 11 postscript figures Equation numbers were corrected, Apj 529(2000) No.1 in pres

The two-parameter Poisson--Dirichlet point process

The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the associated point process (that is, the random point process obtained by regarding the masses as points in the positive real line) is given in terms of the correlation functions. Using this, we apply the theory of point processes to reveal the mathematical structure of the two-parameter Poisson--Dirichlet distribution. Also, developing the Laplace transform approach due to Pitman and Yor, we are able to extend several results previously known for the one-parameter case. The Markov--Krein identity for the generalized Dirichlet process is discussed from the point of view of functional analysis based on the two-parameter Poisson--Dirichlet distribution.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ180 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm