#71. Temporarily free online access to PTRF

Springer is offering free online access to Probability Theory and Related Fields here.

This is valid until Aug 31st 2009.

PTRF is a top journal (maybe the top journal) in Probability Theory, so go ahead and have a look.

#70. New paper by Grigorii Melnichenko

Stop the press, here comes an unexpected paper!

JMVA is going to publish yet another fuzzy paper; particularly, a paper on quantum logic.

Grigorii Melnichenko. Energy discriminant analysis, quantum logic, and fuzzy sets. Journal of Multivariate Analysis, to appear. Update: JMVA 101 (2010), 68-76.

As you may or may not know, broadly speaking there are two main approaches to what a physicist might call non-Kolmogorovian probability. One uses operator-valued probabilities and has led to a quite fruitful field of research called non-commutative or free probability. The other goes back to work by Birkhoff and von Neumann in the 30's, and uses real-valued probabilities but defined on structures poorer than sigma-algebras (e.g. orthomodular lattices; in the original work, events are defined as closed subspaces of a Hilbert space).

While the first-mentioned approach has found strong supporters among statisticians, notably Richard Gill (who has a lot of interesting work on `quantum statistics'), I had never seen a paper from the second strand in a Statistics journal (only in Theoretical Physics journals). But there's a first time for everything...

#69. New paper by Steven Vickers

The connection between this paper and the topics covered in this blog could admittedly not be evident.

Steven Vickers. Fuzzy sets and geometric logic. Fuzzy Sets and Systems, to appear.

The paper follows up Höhle's recent papers (already mentioned here) on the relationship between fuzzy sets and sheaves.

The reason why I am, in a broad sense, interested in this may be clearer in the following paper.

Steven Vickers (2007). Locales and toposes as spaces. In: Marco Aiello, Ian E. Pratt Hartmann, and Johan F.A.K. van Benthem, editors, Handbook of Spatial Logics, 429-496 (chapter 8). Springer.

Sooner or later, we will all formalize events using those and similar tools.

#68. New book by Krzysztof Burdzy

I have randomly learnt that Burdzy has found a publisher for his book

Krzysztof Burdzy (2009). The search for certainty. On the clash of science and philosophy of probability. World Scientific.

(before that, it was available at his website for some time).


Here at the publisher's website for the book, you can download some material, including the introduction chapter.

Here at the author's website, you can find further material including a link to the book's blog and a promotional code for a 20% discount if you buy the book before August 31st.