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A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy.
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The asymptotic order of the random k-SAT threshold
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Stein, E. M., and Shakarchi, R · 2003
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The threshold for random k k -SAT is 2 k log 2 − O ( k ) 2^{k}\log 2-O(k)
Achlioptas, D., and Peres, Y · 2004
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The two possible values of the chromatic number of a random graph
Achlioptas, D., and Naor, A · 2005
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Random k k -SAT: a tight threshold for moderately growing k k
Frieze, A., and Wormald, N. C · 2005
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Random k k -SAT: two moments suffice to cross a sharp threshold
Achlioptas, D., and Moore, C · 2006
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On the maximum satisfiability of random formulas
Achlioptas, D., Naor, A., and Peres, Y · 2007
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Potukuchi, A · 2018
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Storage capacity in symmetric binary perceptrons
Aubin, B., Perkins, W., and Zdeborová, L · 2019
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An algorithm for Komlós conjecture matching Banaszczyk’s bound
Bansal, N., Dadush, D., and Garg, S · 2019
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Capacity lower bound for the Ising perceptron
Ding, J., and Sun, N · 2019
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On the Beck-Fiala conjecture for random set systems
Ezra, E., and Lovett, S · 2019
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A Fourier-analytic approach for the discrepancy of random set systems
Hoberg, R., and Rothvoss, T · 2019
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MacRury, C., Masařík, T., Pai, L., and Pérez-Giménez, X · 2021
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