5 papers · 1 filter
On the Effect of Bottlenecks in Block Spin Models
Isabel Lammers, Matthias Löwe
We study a bottleneck spin model with spins, split into two Curie-Weiss models at low temperature with a bottleneck between them. We propose multiple ways of how to realize suc…
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…
The infinite block spin Ising model
Jonas Jalowy, Isabel Lammers, Matthias Löwe
We study a block mean-field Ising model with spins split into blocks, with Curie-Weiss interaction within blocks and nearest-neighbor coupling between blocks. While previ…
High-Temperature Increasing Propagation of Chaos and its breakdown for the Hopfield Model
Matthias Löwe
We analyze increasing propagation of chaos in the high temperature regime of a disordered mean-field model, the Hopfield model. We show that for (the true high temperature r…
Spectral properties of the stochastic block model and their application to hitting times of random walks
Matthias Löwe, Sara Terveer
We analyze hitting times of simple random walk on realizations of the stochastic block model. We show that under some natural assumptions the hitting time averaged over the target…