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Category Archives: Probability
Tao’s Proof of (logarithmically averaged) Chowla’s conjecture for two point correlations
The Liouville function is the completely multiplicative function with for every prime . The Chowla conjecture predicts that this function behaves randomly. Here is a version of this conjecture. Conjecture 1 (Chowla) For every finite set , This conjecture received … Continue reading
Posted in Number Theory, Probability
Tagged Chowla, Entropy, Logarithmic Averages, primes, Tao
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Optimal intersectivity
In ergodic Ramsey theory, one often wants to prove that certain dynamically defined sets in a probability space intersect (or “recur”) in non-trivial ways. Typically, this is achieved by studying the long term behavior of the sets as the dynamics … Continue reading
Posted in Combinatorics, Probability, Ramsey Theory, Tool
Tagged Bergelson, Dodos, Kanallopoulos, Poincare, Tyros
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