Log-concave sequences are nonnegative real number sequences that satisfy the condition ai2 ≥ ai−1ai+1 for 0 < i < n. They are also known as Pólya Frequency sequences of order 2 (PF2 sequences). Examples of log-concave sequences include binomial coefficients and elementary symmetric means.
Stanford University
Autumn 2022
The course addresses both classic and recent developments in counting and sampling. It covers counting complexity, exact counting via determinants, sampling via Markov chains, and high-dimensional expanders.
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