THE TWO-TYPE RICHARDSON MODEL IN THE HALF-PLANE

• The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for infinite coexistence, while for types with different intensities, it is conjectured that infinite coexistence is not possible. In this paper we study the two-type Richardson model in the upper half-plane Z x Z(+), and prove that coexistence of two types starting on the horizontal axis has positive probability if and only if the types have the same intensity.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Richardson's model

first-passage percolation

competing growth

coexistence

Busemann function

Publication and Content Type

ref (subject category)

art (subject category)