Nica and Speicher: Lectures on the Combinatorics of Free Probability

  • A. Nica, R. Speicher: Lectures on the combinatorics of free probability, London Mathematical Society Lecture Note Series, Vol. 335, Cambridge University Press, 2006
  • Here is a pdf-version by the authors of the book. (Update, May 28, 2020: the old version of the pdf-file differed from the published book by a different numbering of the pages; this old version has now been replaced by a new one which has the same page numbers as the book.)
  • Every good book has its typos, so here are ours. It is quite likely that this list will grow over the course of time (the last update is from January 11, 2026)
    • In Eq. (5.6): \varphi(a_1b_2a_2b_2) should be \varphi(a_1b_1a_2b_2) (page 71)page 84, second displayed equation: the second a_1 should be a b_1
    • page 119, first displayed equation and the line before and the line after: V_m=\{r\} should be V_m=\{p\} and correspondingly a_r should be a_{r(p)}
    • page 168, line -4: v_{s+1}=n should be v_{s+1}=n+1
    • in Eq. (11.8): the subscript \pi should be \sigma (page 176)
    • page 188, first displayed equation (without a number) in the proof of Proposition 11.25: in the sum over \pi add that the blocks of \pi have to be even
    • in Eq. (11.16): in the definition of the set on the left-hand side add that all blocks of \pi are even (page 188)
    • in Eq. (12.14): in the case 0\leq \lambda\leq 1, the density part is \tilde \nu, and not \lambda \tilde \nu (page 204)
    • on line -3 of p. 205 (in part (2) of Remark 12.14): “non-crossing pairings of a set of n elements” should read “non-crossing *partitions* of a set of n elements”
    • in Eq. (15.7): the last \beta should be an \alpha; i.e., \beta_{\vert V_r\vert} should be replaced by \alpha_{\vert V_r\vert} (page 242)
    • page 242, displayed equation in the proof of Proposition 15.6: in the sum over \pi add that the blocks of \pi have to be even; add this condition for \pi also in the following sentence “In that proof it was shown …”
    • in Exercise 19.26, the hypothesis should be changed to a being standard semicircular (instead of a^2=1; the freeness between a and b and the distribution of b (i.e., b^2=1) stay the same (page 317)
    • in Example 22.34, the cycle (4) is missing in \gamma \pi (page 376)