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math.PR2026
A mathematical analysis of hierarchical Hopfield models
Markus Heydenreich, Christian Hirsch, Matthias Löwe
The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden layers? To this end, we develop a formalism of s…
math.PR2025
Mean-field behaviour of the random connection model on hyperbolic space
Matthew Dickson, Markus Heydenreich
We study the random connection model on hyperbolic space in dimension . Vertices of the spatial random graph are given as a Poisson point process with intensi…
math.PR2024
Planar reinforced -out percolation
Gideon Amir, Markus Heydenreich, Christian Hirsch
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses incident edges, whose weight is th…