Extreme Fluctuations & Correlated Random Matrices
Group leader
Specific themes and goals
- Extreme-value physics in correlated systems: We develop theory and numerics to understand how rare events and extremes emerge when degrees of freedom are strongly correlated over long distances (beyond i.i.d. extreme-value theory).
- Long-range correlated random matrices: We construct and analyze random-matrix ensembles with structured long-range correlations and show how increasing correlation strength can drive qualitative changes in spectral statistics (heavy tails ↔ Gaussian ↔ classical limits).
- Criticality, percolation, and geometry: We use percolation and critical phenomena to connect stochastic geometry (clusters and interfaces) to universality, scaling, and measurable large deviations in complex media.
- Dimensional reduction in critical matter: We study how higher-dimensional critical systems (e.g., Ising and spin-glass settings) can admit effective lower-dimensional descriptions and emergent universality.
- Data-informed complex systems applications: We bridge rigorous statistical-physics theory with real data (e.g., climate variability and other correlated multivariate systems) using interpretable, physics-grounded models.
Group composition & projects/funding
- Group leader: Prof. Dr. Abbas Ali Saberi
- Group composition: The group supervises BSc/MSc theses, PhD projects, and postdoctoral research in theoretical and computational statistical physics, with close links to international collaborators and institutes.
- Funding / projects: Core support comes through the DFG Heisenberg Programme (Heisenberg Professorship), enabling the development of a focused research team and a coherent long-term program on correlated random matrices, percolation, criticality, and extreme fluctuations (DFG project listed “term since 2025”, project number 557852701).
Selected publications
- q-Gaussian Crossover in Overlap Spectra toward 3D Edwards–Anderson Criticality — Phys. Rev. Lett. 136, 087103 (2026) — DOI: 10.1103/sdbx-wx5t.
- Emergence of Rigidity Percolation in Flowing Granular Systems — Science Advances 9(35), eadh5586 (2023) — DOI: 10.1126/sciadv.adh5586.
- Unified modeling and experimental realization of electrical and thermal percolation in polymer composites — Applied Physics Reviews 9, 041403 (2022) — DOI: 10.1063/5.0089445.
- Universal gap scaling in percolation — Nature Physics 16(4), 455–461 (2020) — DOI: 10.1038/s41567-019-0783-2.
- Evidence for an ancient sea level on Mars — ApJL 896, L25 (2020) — DOI: 10.3847/2041-8213/ab982d.
- Competing universalities in KPZ growth models — Phys. Rev. Lett. 122, 040605 (2019) — DOI: 10.1103/PhysRevLett.122.040605.
- Recent advances in percolation theory and its applications — Physics Reports 578, 1–32 (2015) — DOI: 10.1016/j.physrep.2015.03.003.
- Percolation description of the global topography of Earth and the Moon — Phys. Rev. Lett. 110, 178501 (2013) — DOI: 10.1103/PhysRevLett.110.178501.
- Three-dimensional Ising model, percolation theory and conformal invariance — Europhys. Lett. 92, 67005 (2010) — DOI: 10.1209/0295-5075/92/67005.
Honors and Awards
| 2025 – Present | DFG Heisenberg Programme (Heisenberg Fellowship / Heisenberg Professorship) |
| 2024 – 2025 | Leadership of the Advanced Study Group at MPI-PKS |
| 2016 – 2018 | Alexander von Humboldt Research Fellowship Award Host: Prof. Martin Zirnbauer, Institute for Theoretical Physics, University of Cologne, Germany |
| 2013 – 2019 | Research Associate Award, ICTP, Italy |
| December 2020 | Selected as a “Distinguished Young Researcher”, 29th Research and Technology Festival, University of Tehran |
| 2016 | Abu Rayhan Al-Biruni Award for “Outstanding Young Researcher in Physics”, Academy of Sciences of Iran |
| 2016 | Selected as “Top Training Teacher”, 3rd Education Festival, University of Tehran |
| 2015 – Present | Elected annually as a member of the Iran’s Scientific Elite Federation (ISEF) |
| 2014 – 2015 | Voted as “Popular Professor” by students of the Physics Department, University of Tehran |
| 2014 | Distinguished International Researcher of the Year, University of Tehran |
| 2009 | The Khwarizmi Youth Research Award — selected nationwide |