TY  - JOUR
A1  - Eliazar, Iddo
A1  - Metzler, Ralf
A1  - Reuveni, Shlomi
T1  - Gumbel central limit theorem for max-min and min-max
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - The max-min and min-max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the max-min and min-max is challenging as matrices are large and full information about their entries is lacking. Here we take a statistical-physics approach and establish limit laws—akin to the central limit theorem—for the max-min and min-max of large random matrices. The limit laws intertwine random-matrix theory and extreme-value theory, couple the matrix dimensions geometrically, and assert that Gumbel statistics emerge irrespective of the matrix entries' distribution. Due to their generality and universality, as well as their practicality, these results are expected to have a host of applications in the physical sciences and beyond.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48366
SN  - 2470-0045
SN  - 2470-0053
VL  - 100
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  -