Stein's method for dependent random variables occurring in Statistical Mechanics (2009)
Eichelsbacher, Peter, Löwe, Matthias
We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in...
On the Storage Capacity of Hopfield Models with Spatially Correlated Patterns (2007)
We analyze the storage capacity of the Hopfield model with spatially correlated patterns ¸ i (i.e. the patterns ¸ themselves are independent but have correlated components ¸ i ). We show that the...
The Storage Capacity of Generalized Hopfield Models with Semantically Correlated Patterns (2007)
We analyze the storage capacity of a variant of the Hopfield model with semantically correlated patterns ¸ i (that is the patterns ¸ themselves are correlated but consist of independent components...
Edge Search In Graphs And Hypergraphs (2007)
Ingo Althöfer, Matthias Löwe, Matthias L Owe
Consider an undirected hypergraph H = (X; E) with a probability distribution P on the set E of its hyperedges. We investigate the average case complexity L(H;P ) of finding an unknown hyperedge e 2 E...
Workshop On PROBABILITY THEORY and its APPLICATIONS (2007)
Peter Eichelsbacher, Matthias Löwe (Eds.), Matthias Lowe, M. Grunwald, W. Konig
. Well-known inequalities for the spectral gap of a Markov chain, like Poincar'e's and Cheeger's Inequality, do not perform well if the transition graph of the Markov chain is strongly...
Workshop On PROBABILITY THEORY and its APPLICATIONS (2007)
Peter Eichelsbacher, Matthias Löwe, Anton Bovier, Julia Brettschneider
. We investigate the fluctuations of the mean magnetization in a Curie -- Weiss model with ferromagnetic random couplings. In the high-temperature region, the limiting fluctuations as the system size...
Reconstructing a multicolor random scenery seen along a random walk path with bounded jumps (2004)
Matthias Löwe, Heinrich Matzinger, Franz Merkl
Kesten [12] noticed that the scenery reconstruction method proposed by Matzinger [17] relies heavily on the skip-free property of the random walk. He asked if one can still reconstruct an i.i.d....
Scenery reconstruction in two dimensions with many colors (2002)
Löwe, Matthias, Matzinger, Heinrich
Kesten has observed that the known reconstruction methods of random sceneries seem to strongly depend on the one-dimensional setting of the problem and asked whether a construction still is possible...
Fluctuations of the free energy in the REM and the $p$-spin SK models (2002)
Bovier, Anton, Kurkova, Irina, Löwe, Matthias
We consider the random fluctuations of the free energy in the $p$-spin version of the Sherrington–Kirkpatrick (SK) model in the high-temperature regime. Using the martingale approach of Comets and...
Fluctuations in the Hopfield model at the critical temperature (1999)
We investigate the fluctuation...
We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks with finitely many patterns at the critical temperature 1=fi c = 1. At the...
On the storage capacity of Hopfield models with correlated patterns (1998)
We analyze the storage capacity of the Hopfield model with correlated patterns $(\xi_i^{\nu})$. We treat both the case of semantically and spatially correlated patterns (i.e., the patterns are either...
Large Deviations For Partial Sums U-Processes (1997)
Peter Eichelsbacher, Matthias Löwe, Matthias L Owe
. The large deviations principle (LDP) is known to hold for U-statistics of real valued kernel functions of Polish space valued i. i. d. random variables, where moreover appropriate exponential tail...
On the Storage Capacity of the Hopfield Model with Biased Patterns (1996)
We introduce a form of the Hopfield model that is able to store an increasing number of biased i.i.d. patterns (it is well known that the standard Hopfield model fails to work properly in this...
On the Storage Capacity of Hopfield Models with Weakly Correlated Patterns (1996)
We analyze the storage capacity of different forms of the Hopfield model with semantically correlated patterns ¸ i (i.e. the patterns are correlated in but independent in i). We show that the...
On A Randomized Version Of Parallel Local Search (1995)
We introduce a stochastic version of the parallel local search algorithm. Using techniques similar to those used to establish convergence of the simulated annealing algorithm we are able to give a...
Simulated Annealing with Time dependent Energy Function via Sobolev inequalities (1994)
We analyze the Simulated Annealing Algorithm with an energy function U t that depends on time. Assuming some regularity conditions on U t (especially that U t does not change too quickly in time),...
Stochastic Search on Graphs and Genetic Algorithms (1994)
We analyze the convergence of a wide class of Genetic Algorithms by reducing them to a class of stochastic search algorithms on graphs. We show that, if the underlying random walk is irreducible and...
The capacity of q-state Potts neural networks with parallel retrieval dynamics
Löwe, Matthias, Vermet, Franck
We define a Potts version of neural networks with q states. We give upper and lower bounds for the storage capacity of this model of associative memory in the sense of exact retrieval of the stored...
The storage capacity of the Hopfield model and moderate deviations
Löwe, Matthias, Vermet, Franck
This note relates the storage capacity of the Hopfield model of neural networks with possibly correlated patterns to a moderate deviation upper bound for the empirical correlation of the patterns....
On the invariant measure of non-reversible simulated annealing
We give a criterion to ensure convergence of non-reversible simulated annealing algorithms to the set of global minima of the target function U. We show, that such conditions only have to take into...
We show a principle of large deviations for sums of random variables which themselve obey a principle of large deviations with speed an and rate function I. The new rate function is again given by I,...