Prof. Dr. Matthias Löwe

Topics in Mathematics Münster

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.

• Bovier, Anton; Kurkova, Irina; Löwe, Matthias Fluctuations of the free energy in the REM and the p-spin SK models. Annals of Probability Vol. 30 (2), 2002, pp 605--651 online
• Friesen, Olga; Löwe, Matthias A phase transition for the limiting spectral density of random matrices. Electronic Journal of Probability Vol. 18, 2013 online
• Gantert, Nina; Löwe, Matthias; Steif, Jeffrey E. The voter model with anti-voter bonds. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Vol. 41 (4), 2005, pp 767--780 online
• Jalowy, Jonas; Kabluchko, Zakhar; Löwe, Matthias; Marynych, Alexander When does the chaos in the Curie-Weiss model stop to propagate?. Electronic Journal of Probability Vol. 28, 2023 online
• Kabluchko, Zakhar; Löwe, Matthias; Schubert, Kristina Fluctuations of the magnetization for Ising models on Erdos-Rényi random graphs — the regimes of small p and the critical temperature. Journal of Physics A: Mathematical and Theoretical Vol. 53, 2020, pp 355004, 37 online
• Kabluchko, Zakhar; Löwe, Matthias; Schubert, Kristina Fluctuations for the partition function of Ising models on Erdos-Rényi random graphs. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Vol. 57 (4), 2021 online
• Kabluchko, Zakhar; Löwe, Matthias; Schubert, Kristina Fluctuations of the magnetization for Ising models on Erdos-Rényi random graphs — the regimes of low temperature and external magnetic field. Latin American Journal of Probability and Mathematical Statistics Vol. 19, 2022 online
• Löwe, Matthias; Matzinger III, Heinrich Scenery reconstruction in two dimensions with many colors. Annals of Applied Probability Vol. 12 (4), 2002, pp 1322--1347 online
• Löwe, Matthias; Merkl, Franz Moderate deviations for longest increasing subsequences: the upper tail. Communications on Pure and Applied Mathematics Vol. 54 (12), 2001, pp 1488--1520 online
• Löwe, Matthias; Schubert, Kristina Exact recovery in block spin Ising models at the critical line. Electronic Journal of Statistics Vol. 14 (1), 2020, pp 1796-1815 online

Recent Publications of Prof. Dr. Matthias Löwe

$\bullet $ Zakhar Kabluchko and Matthias Löwe. Propagation of chaos in the random field Curie–Weiss model. Journal of Statistical Mechanics: Theory and Experiment, 2024(11):113206, November 2024. doi:10.1088/1742-5468/ad8f2a.

$\bullet $ Jonas Jalowy, Zakhar Kabluchko, and Matthias Löwe. Propagation of chaos and residual dependence in gibbs measures on finite sets. arXiv e-prints, October 2024. arXiv:2410.08004.

$\bullet $ Raphael Lafargue, Luke Smith, Franck Vermet, Mathias Löwe, Ian Reid, Vincent Gripon, and Jack Valmadre. Oops, I sampled it again: Reinterpreting confidence intervals in few-shot learning. arXiv e-prints, September 2024. arXiv:2409.02850.

$\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? Electronic Journal of Probability, January 2023. doi:10.1214/23-ejp1039.

$\bullet $ Matthias Löwe and Sara Terveer. A central limit theorem for the mean starting hitting time for a random walk on a random graph. J. Theor. Probab., 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 $ 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 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. J. Phys. A: Math. Theor., 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. J. Stat. Phys., 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 Oper. Stoch. Equ., 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. J. Theor. Probab., 32(2):872–897, February 2019. doi:10.1007/s10959-019-00881-5.