Fraser Watts (ed.), Creation: Law and Probability

On the Percolation Bcft and the Crossing Probability of Watts

The logarithmic conformal field theory describing critical percolation is further explored using Watts’ determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition changing operator which governs Watts’ computation is identified with a primary field which does not fit naturally within the extended Kac table. Instead a “shift...

Zipf's law and L. Levin's probability distributions

Zipf’s law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation. In this paper I suggest that at least in certain situations, Zipf’s law can be explained as a special case of the a priori distribution introduced and studied...

Probability and Statistics in the Law

Noisy probability judgment, the conjunction fallacy, and rationality: Comment on Costello and Watts (2014).

According to Costello and Watts (2014), probability theory can account for key findings in human judgment research provided that random noise is embedded in the model. We concur with a number of Costello and Watts's remarks, but challenge the empirical adequacy of their model in one of their key illustrations (the conjunction fallacy) on the basis of recent experimental findings. We also discus...

Exploring Watts’ Cascade Boundary

! z . In this paper we study cascades on finite networks in this upper boundary region via simulations. We distinguish two kinds of cascades: total network cascades (or TNCs) that essentially consume the entire finite network, and cascades corresponding to those predicted by percolation theory that consume only the initially struck vulnerable clusters and possibly a few others. We show that the...