A new mathematical proof resolves a 35-year-old bet between Noga Alon and Peter Sarnak regarding the prevalence of optimal expander graphs, demonstrating that both mathematicians were partially incorrect. The proof, building on work in random matrix theory, reveals that approximately 69% of regular graphs are Ramanujan graphs.
Explores the role of conditional probability in understanding events and Bayes' theorem, with examples in regression analysis and everyday scenarios, demonstrating how our biological tissue runs probabilistic machinery.
The second law of thermodynamics is among the most sacred in all of science, but it has always rested on 19th century arguments about probability. New arguments trace its true source to the flows of quantum information.
analogue I-K of the Laplacian in potential theory
