ar X iv : m at h / 06 07 13 1 v 2 [ m at h . PR ] 8 J an 2 00 7 PERCOLATION IN A HIERARCHICAL RANDOM GRAPH

ar X iv : 0 70 5 . 05 06 v 1 [ m at h . PR ] 3 M ay 2 00 7 Space – time percolation

The contact model for the spread of disease may be viewed as a directed percolation model on Z×R in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly complete analysis of the contact model at and near its critical point. The corresponding process when the time-axis is unoriented is an undirected percolation model to which...

ar X iv : h ep - p h / 06 08 05 0 v 1 4 A ug 2 00 6 Percolation and high energy cosmic rays above 10 17 eV

ar X iv : m at h / 06 07 13 0 v 1 [ m at h . A G ] 5 J ul 2 00 6 TWISTED LOOP GROUPS AND THEIR AFFINE FLAG VARIETIES

ar X iv : 0 80 7 . 06 87 v 1 [ m at h . PR ] 4 J ul 2 00 8 Representations of SO ( 3 ) and angular polyspectra

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S 2 = ˘ (x, y, z) : x 2 + y 2 + z 2 = 1 ¯. Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and Clebsch-Gordan coefficients. The findings of the present paper constitute a basis upon which one can build formal proced...

ar X iv : m at h / 06 01 33 8 v 2 [ m at h . D S ] 1 3 A pr 2 00 6 HYPERBOLIC OUTER BILLIARDS : A FIRST EXAMPLE

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.