Poisson cylinders in hyperbolic space

• We consider the Poisson cylinder model in d-dimensional hyperbolic space. We show that in contrast to the Euclidean case, there is a phase transition in the connectivity of the collection of cylinders as the intensity parameter varies. We also show that for any non-trivial intensity, the diameter of the collection of cylinders is infinite.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Poisson cylinders

hyperbolic space

continuum percolation

RANDOM INTERLACEMENTS

PERCOLATION

PLANE

Statistics & Probability

RANDOM INTERLACEMENTS

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