Projects in Mathematics Muenster
Research Interests

Research Interests

$\bullet$ Statistical mechanics.
$\bullet$ Neural networks and models of associative memories.
$\bullet$ Spin glasses.
$\bullet$ Large and moderate deviations.
$\bullet$ Markov chains and Markov chain Monte Carlo methods.
$\bullet$ Random walk in random scenery.
$\bullet$ Random matrix theory.

Selected Publications

Selected Publications of Matthias Löwe

$\bullet$ P. Eichelsbacher and M. Löwe. Lindeberg's method for moderate deviations and random summation. J. Theoret. Probab. (to appear), 2018.

$\bullet$ M. Löwe and F. Vermet. Capacity of an associative memory model on random graph architectures. Bernoulli, 21(3):1884–1910, 2015.

$\bullet$ M. Ebbers, H. Knöpfel, M. Löwe, and F. Vermet. Mixing times for the swapping algorithm on the Blume- Emery- Griffiths model. Random Structures Algorithms, 45(1):38–77, 2014.

$\bullet$ O. Friesen and M. Löwe. A phase transition for the limiting spectral density of random matrices. Electron. J. Probab., 18:no. 17, 17 pp., 2013.

$\bullet$ M. Löwe, H. Matzinger, and F. Merkl. Reconstructing a multicolor random scenery seen along a random walk path with bounded jumps. Electron. J. Probab., 9:no. 15, 436–507, 2004.

$\bullet$ M. Löwe and H. Matzinger. Scenery reconstruction in two dimensions with many colors. Ann. Appl. Probab., 12(4):1322–1347, 2002.

$\bullet$ A. Bovier, I. Kurkova, and M. Löwe. Fluctuations of the free energy in the {REM} and the $p$-spin {SK} models. Ann. Probab., 30(2):605–651, 2002.

$\bullet$ M. Löwe and F. Merkl. Moderate deviations for longest increasing subsequences: the upper tail. Comm. Pure Appl. Math., 54(12):1488–1520, 2001.

$\bullet$ B. Gentz and M. Löwe. The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature. Probab. Theory Related Fields, 115(3):357–381, 1999.

$\bullet$ M. Löwe. On the storage capacity of Hopfield models with correlated patterns. Ann. Appl. Probab., 8(4):1216–1250, 1998.

Current Publications

$\bullet$ M. Ebbers and M. Löwe. Equi-energy sampling does not converge rapidly on the mean-field Potts model with three colors close to the critical temperature. Journal of Physics A: Mathematical and Theoretical, February 2020. doi:10.1088/1751-8121/ab7422.

$\bullet$ A. Helali and M. Löwe. Hitting times, commute times, and cover times for random walks on random hypergraphs. Statistics & Probability Letters, 154:108535, 6, November 2019. URL: https://doi.org/10.1016/j.spl.2019.06.011, doi:10.1016/j.spl.2019.06.011.

$\bullet$ Z. Kabluchko, M. Löwe, and K. Schubert. Fluctuations of the magnetization for Ising models on dense Erdős–Rényi random graphs. Journal of Statistical Physics, 177(1):78–94, August 2019. URL: https://ui.adsabs.harvard.edu/abs/2019JSP...tmp..177K, doi:10.1007/s10955-019-02358-5.

$\bullet$ J. Liu and M. Löwe. Moderate deviations for the size of the giant component in a random hypergraph. arXiv e-prints, July 2019. arXiv:1907.07834.

$\bullet$ M. Löwe and K. Schubert. On the limiting spectral density of random matrices filled with stochastic processes. Random Operators and Stochastic Equations, 27(2):89–105, June 2019. URL: https://doi.org/10.1515/rose-2019-2008, doi:10.1515/rose-2019-2008.

$\bullet$ M. Löwe and K. Schubert. Exact recovery in block spin Ising models at the critical line. arXiv e-prints, May 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190600021L, arXiv:1906.00021.

$\bullet$ M. Löwe, K. Schubert, and F. Vermet. Multi-group binary choice with social interaction and a random communication structure - a random graph approach. arXiv e-prints, April 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190411890L, arXiv:1904.11890.

$\bullet$ M. Ebbers and M. Löwe. Equi-Energy sampling does not converge rapidly on the Potts model close to the critical temperature. arXiv e-prints, March 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190400394E, arXiv:1904.00394.

$\bullet$ H. Knöpfel, M. Löwe, K. Schubert, and A. Sinulis. Fluctuation results for general block spin Ising models. arXiv e-prints, February 2019. URL: https://ui.adsabs.harvard.edu/abs/2019arXiv190202080K, arXiv:1902.02080.

$\bullet$ P. Eichelsbacher and M. Löwe. Lindeberg's method for moderate deviations and random summation. Journal of Theoretical Probability, 32(2):872–897, February 2019. arXiv:1705.03837, doi:10.1007/s10959-019-00881-5.