890 citations · 8.4k across the 209 of their papers we have counts for
210 papers
Leaves of preferential attachment trees
Harrison Hartle, P. L. Krapivsky
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented w…
Statistics of leaves in growing random trees
Harrison Hartle, P. L. Krapivsky
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fractio…
Dynamics of feedback Ising model
Yi-Ping Ma, Ivan Sudakow, P. L. Krapivsky +1
We study the dynamics of a mean-field Ising model whose coupling depends on the magnetization via a linear feedback function. A key feature of this linear feedback Ising model (FIM…
Mixed phases in feedback Ising models
Yi-Ping Ma, Ivan Sudakow, P. L. Krapivsky
We study mean-field Ising models in which the coupling depends on the magnetization via a feedback function. We identify mixed phases (MPs) and show that they can be stable at zero…
Random Maps with Sociological Flavor
P. L. Krapivsky
A map of a set to itself admits a representation by a graph with vertices being the elements of the set and an edge between every vertex and its image. Communities defined as the m…
Random Recursive Hypergraphs
P. L. Krapivsky
Random recursive hypergraphs grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, an…