115 citations · 199 across the 26 of their papers we have counts for
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When does propagation of chaos in the critical Curie-Weiss model stop?
Nina Gantert, Matthias Löwe, Kilian Schnappinger
We study increasing propagation of chaos for the critical Curie- Weiss model (i.e. the mean-field Ising model at critical inverse temperature 1, with no external field). We give a…
On associative neural networks for sparse patterns with huge capacities
Matthias Löwe, Franck Vermet
Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the…
Propagation of chaos in the Random field Curie-Weiss model
Matthias Löwe, Zakhar Kabluchko
We prove propagation of chaos in the Random field mean-field Ising model, also known ad the Random field Curie-Weiss model. We show that in the paramagnetic phase, i.e.\ in the reg…
When does the chaos in the Curie-Weiss model stop to propagate?
Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe +1
We investigate increasing propagation of chaos for the mean-field Ising model of ferromagnetism (also known as the Curie-Weiss model) with spins at inverse temperature an…
A Central Limit Theorem for the average target hitting time for a random walk on a random graph
Matthias Löwe, Sara Terveer
Consider a simple random walk on a realization of an Erdős-Rényi graph. Assume that it is asymptotically almost surely (a.a.s.) connected. Conditional on an eigenvector delocalizat…
Fluctuations of the magnetization in the Block Potts Model
Jonas Jalowy, Matthias Löwe, Holger Sambale
In this note we study the block spin mean-field Potts model, in which the spins are divided into blocks and can take different values (colors). Each block is allowed t…
Reconstructing a (recurrent) random environment from a single trajectory of Random Walk in Random Environment with errors
Jonas Jalowy, Matthias Löwe
We consider one infinite path of a Random Walk in Random Environment (RWRE, for short) in an unknown environment. This environment consists of either i.i.d.\ site or bond randomnes…
A Central Limit Theorem for the mean starting hitting time for a random walk on a random graph
Matthias Löwe, Sara Terveer
We consider simple random walk on a realization of an Erdős-Rényi graph that is asymptotically almost surely (a.a.s.) connected. We show a Central Limit Theorem (CLT) for the avera…
Fluctuations of the Magnetization for Ising Models on Erdős-Rényi Random Graphs -- the Regimes of Small p and the Critical Temperature
Zakhar Kabluchko, Matthias Löwe, Kristina Schubert
We continue our analysis of Ising models on the (directed) Erdős-Rényi random graph. This graph is constructed on vertices and every edge has probability to be present. The…
Fluctuations of the Magnetization for Ising Models on Dense Erdős-Rényi Random Graphs
Zakhar Kabluchko, Matthias Löwe, Kristina Schubert
We analyze Ising/Curie-Weiss models on the (directed) Erdős-Rényi random graph on vertices in which every edge is present with probability . These models were introduced by…
Equi-Energy sampling does not converge rapidly on the mean-field Potts model with three colors close to the critical temperature
Mirko Ebbers, Matthias Löwe
Equi-Energy Sampling (EES, for short) is a method to speed up the convergence of the Metropolis chain, when the latter is slow. We show that there are still models like the mean-fi…
Fluctuation results for general block spin Ising models
Holger Knöpfel, Matthias Löwe, Kristina Schubert +1
We study a block spin mean-field Ising model, i.e. a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed proportion of ve…
Lindeberg's method for moderate deviations and random summation
Peter Eichelsbacher, Matthias Löwe
We apply Lindeberg's method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate…
On a model of associative memory with huge storage capacity
Mete Demircigil, Judith Heusel, Matthias Löwe +2
In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function an…
On the Limiting Spectral Density of Random Matrices filled with Stochastic Processes
Matthias Löwe, Kristina Schubert
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent…
A Comparative Study of Sparse Associative Memories
Vincent Gripon, Judith Heusel, Matthias Löwe +1
We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of s and s with about s, only. We compare…
On the capacity of a new model of associative memory based on neural cliques
Judith Heusel, Matthias Löwe, Franck Vermet
Based on recent work by Gripon and Berrou, we introduce a new model of an associative memory. We show that this model has an efficiency bounded away from 0 and is therefore signifi…
Large deviation upper bounds for sums of positively associated indicators
Matthias Löwe, Franck Vermet
We give exponential upper bounds for , in particular , where is a sum of indicator random variables that are positively associated. These bounds allow, in p…
On hitting times for simple random walk on dense Erdös-Rényi random graphs
Matthias Löwe, Felipe Torres
Let be an Erdös-Rényi random graph and be a simple random walk on it. We study the the order of magnitude of w…
Capacity of an associative memory model on random graph architectures
Matthias Löwe, Franck Vermet
We analyze the storage capacity of the Hopfield models on classes of random graphs. While such a setup has been analyzed for the case that the underlying random graph model is an E…
Mixing times for the Swapping Algorithm on the Blume-Emery-Griffiths Model
M. Ebbers, H. Knöpfel, M. Löwe +1
We analyze the so called Swapping Algorithm, a parallel version of the well-known Metropolis-Hastings algorithm, on the mean-field version of the Blume-Emery-Griffiths model in sta…
Moderate deviations for random field Curie-Weiss models
Matthias Löwe, Raphael Meiners
The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens…
A phase transition for the limiting spectral density of random matrices
Olga Friesen, Matthias Löwe
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independen…
Gaussian Fluctuations for Sample Covariance Matrices with Dependent Data
Olga Friesen, Matthias Löwe, Michael Stolz
It is known (Hofmann-Credner and Stolz (2008)) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W_n = 1/n Y_n Y_n^t to the Marčenko-Pa…