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math.PR2012
Emergence of condensation in Kingman's model of selection and mutation
Steffen Dereich, Peter Mörters
We describe the onset of condensation in the simple model for the balance between selection and mutation given by Kingman in terms of a scaling limit theorem. Loosely speaking, thi…
math.PR2011
Typical distances in ultrasmall random networks
Steffen Dereich, Christian Mönch, Peter Mörters
We show that in preferential attachment models with power-law exponent the distance between randomly chosen vertices in the giant component is asymptotically equal to $…
math.PR2008
The Hausdorff dimension of the double points on the Brownian frontier
Richard Kiefer, Peter Morters
The frontier of a planar Brownian motion is the boundary of the unbounded component of the complement of its range. In this paper we find the Hausdorff dimension of the set of doub…