Given a sequence of numbers in , consider the following experiment. First, we flip a fair coin and then, at step , we turn the coin over to the other side with probability , . What can we say about the distribution of the empirical frequency of heads as ?
We show that a number of phase transitions take place as the turning gets slower (i.e. is getting smaller), leading first to the breakdown of the Central Limit Theorem and then to that of the Law of Large Numbers. It turns out that the critical regime is . Among the scaling limits, we obtain some well known special (Uniform, Gaussian, Semicircle and Arcsine) laws.
The talk is intended to a general audience and no expertise in probability is assumed!
This is joint work with S. Volkov (Lund, Sweden)
Turning a coin instead of tossing it
Aug. 30, 2016 1pm (MATH 220)
Agnes Szendrei (CU Boulder)
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The Algebraic Dichotomy Conjecture predicts that the constraint satisfaction problem CSP(A) with a fixed finite template A is in P if the algebra associated to A has a Taylor term. (Otherwise, CSP(A) is known to be NP-complete.)
The goal of this sequence of talks is to discuss a recent theorem of M. Olsak (Charles University) which greatly simplifies the condition "an algebra has a Taylor term". Namely, Olsak proved that if an algebra (finite or infinite) has a Taylor term, then it has a specific Taylor term in 12 variables.