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 of Prof. Dr. 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 Cluster Publications of Prof. Dr. Matthias Löwe
$\bullet $ Matthias Löwe and Sara Terveer. Spectral properties of the strongly assortative stochastic block model and their application to hitting times of random walks. arXiv e-prints, January 2024. arXiv:2401.07896.
$\bullet $ Matthias Löwe and Zakhar Kabluchko. Propagation of chaos in the random field curie-weiss model. arXiv e-prints, December 2023. arXiv:2312.01866.
$\bullet $ Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe, and Alexander Marynych. When does the chaos in the Curie-Weiss model stop to propagate? arXiv e-prints, July 2023. arXiv:2307.05335.
$\bullet $ Matthias Löwe and Sara Terveer. A central limit theorem for the mean starting hitting time for a random walk on a random graph. Journal of Theoretical Probability, August 2022. doi:10.1007/s10959-022-01195-9.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for ising models on Erdős-Rényi random graphs – the regimes of low temperature and external magnetic field. Lat. Am. J. Probab. Math. Stat, 19:537––563, August 2022. doi:10.30757/ALEA.v19-21.
$\bullet $ Jonas Jalowy, Matthias Löwe, and Holger Sambale. Fluctuations of the magnetization in the block Potts model. J. Stat. Phys., 187(1):3, February 2022. doi:10.1007/s10955-022-02889-4.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations for the partition function of Ising models on Erdös–Rényi random graphs. Ann. Inst. Henri Poincaré Probab. Stat., 57(4):2017–2042, November 2021. doi:10.1214/20-aihp1137.
$\bullet $ Matthias Löwe and Sara Terveer. A central limit theorem for incomplete $U$-statistics over triangular arrays. Braz. J. Probab. Stat., 35(3):499–522, August 2021. doi:10.1214/20-BJPS492.
$\bullet $ Arthur Charpentier, Lariosse Kouakou, Matthias Löwe, Philipp Ratz, and Franck Vermet. Collaborative insurance sustainability and network structure. arXiv e-prints, July 2021. arXiv:2107.02764.
$\bullet $ Holger Knöpfel, Matthias Löwe, and Holger Sambale. Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model. Electron. Commun. Probab., 26:Paper No. 29, 14, May 2021. doi:10.1214/21-ecp397.
$\bullet $ Matthias Löwe and Sara Terveer. A central limit theorem for the average target hitting time for a random walk on a random graph. arXiv e-prints, April 2021. arXiv:2104.01053.
$\bullet $ Vicent Gripon, Matthias Löwe, and Franck Vermet. Some remarks on replicated simulated annealing. J. Stat. Phys., 182(3):Paper No. 51, 22, March 2021. doi:10.1007/s10955-021-02727-z.
$\bullet $ Jonas Jalowy and Matthias Löwe. Reconstructing a recurrent random environment from a single trajectory of a random walk in random environment with errors. Electron. Commun. Probab., 26(none):1–12, January 2021. doi:10.1214/21-ECP425.
$\bullet $ Matthias Löwe, Kristina Schubert, and Franck Vermet. Multi-group binary choice with social interaction and a random communication structure-A random graph approach. Phys. A, 556:124735, October 2020. doi:10.1016/j.physa.2020.124735.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for Ising models on Erdős-Rényi random graphs—the regimes of small $p$ and the critical temperature. J. Phys. A, 53(35):355004, 37, August 2020. doi:10.1088/1751-8121/aba05f.
$\bullet $ Matthias Löwe. Reconstructing a (recurrent) random environment from a single trajectory of Random Walk in Random Environment with errors. arXiv e-prints, August 2020. arXiv:2008.12043.
$\bullet $ Matthias Löwe and Kristina Schubert. Exact recovery in block spin Ising models at the critical line. Electron. J. Stat., 14(1):1796–1815, April 2020. doi:10.1214/20-EJS1703.
$\bullet $ Holger Knöpfel, Matthias Löwe, Kristina Schubert, and Arthur Sinulis. Fluctuation results for general block spin Ising models. J. Stat. Phys., 178(5):1175–1200, February 2020. doi:10.1007/s10955-020-02489-0.
$\bullet $ Mriko Ebbers and Matthias 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 $ Amine Helali and Matthias Löwe. Hitting times, commute times, and cover times for random walks on random hypergraphs. Statistics & Probability Letters, 154:108535, 6, November 2019. doi:10.1016/j.spl.2019.06.011.
$\bullet $ Zakhar Kabluchko, Matthias Löwe, and Kristina Schubert. Fluctuations of the magnetization for Ising models on dense Erdős–Rényi random graphs. Journal of Statistical Physics, 177(1):78–94, August 2019. doi:10.1007/s10955-019-02358-5.
$\bullet $ Jingjia Liu and Matthias Löwe. Moderate deviations for the size of the giant component in a random hypergraph. arXiv e-prints, July 2019. arXiv:1907.07834.
$\bullet $ Matthias Löwe and Kristina Schubert. On the limiting spectral density of random matrices filled with stochastic processes. Random Operators and Stochastic Equations, 27(2):89–105, June 2019. doi:10.1515/rose-2019-2008.
$\bullet $ Peter Eichelsbacher and Matthias Löwe. Lindeberg's method for moderate deviations and random summation. Journal of Theoretical Probability, 32(2):872–897, February 2019. doi:10.1007/s10959-019-00881-5.