Last updated May 14, 2013
Topics in random matrix theory.
Publication Year: 2012
Graduate Studies in Mathematics, vol. 132
American Mathematical Society
This continues my series of books derived from my blog. The preceding books in this series were “Structure and Randomness“, “Poincaré’s legacies“, “An epsilon of room“, and “An introduction to measure theory“.
Pre-errata (errors in the draft that were corrected in the published version):
- p. 20: In Exercise 1.1.11(i), “if and only for” should be “if and only if for”.
- p. 21: In Exercise 1.1.18, in the definition of convexity, should be .
- p. 46: In Exercise 1.3.16, Weilandt should be Wielandt. Similarly on p. 47 after Exercise 1.3.9, in Exercise 1.3.22(v) on page 53, on page 137 before (2.82), on page 184 after (2.129), and on page 208 before 2.6.6. Also, before (1.66), the supremum should be over rather than .
- p. 72: All occurrences of on this page should be .
- p. 183: The formula (2.127) should be attributed to Dyson ( The three fold way, J. Math. Phys. vol. 3 (1962) pgs. 1199-1215) rather than to Ginibre. Similarly on pages 251, 259, and 265.
- p. 225-226: U should be U_0 (several occurrences). Also, should be and should be .
- p. 225, Section 2.8.2: right parenthesis should be added after “sufficient decay at infinity.”
- p. 228, just before (2.179): ”g_n” should be “f_n”
- p. 231: ”lets ignore” should be “lets us ignore”
- p. 258: In the second paragraph, should be , and should be .
- Page 22: In Exercise 1.1.18(ii), the requirement that the take values in should be dropped.
- Page 29, In Definition 1.1.23, should lie in rather than .
- Page 51: In Section 1.3.6, the role of rows and columns should be reversed in “at least as many rows as columns”.
- Page 68: In the last display of Proposition 2.1.9, should be .
- Page 76: In the proof of Lemma 2.1.16, after (2.24), the expectation in the next two expressions should instead be conditional expectation with respect to .
- Page 78: In the proof of Proposition 2.1.19, the definitions of and are missing absolute value signs (they should be and respectively).
- p. 81: In Remark 2.2.2, “central limit” should be “central limit theorem”
- Page 97: Near the end of Section 2.2.5: [TaVuKr2010] should be [TaVu2009b].
- Page 98: In the proof of Theorem 2.2.13, should be assumed to be Lipschitz and not just continuous.
- Page 183: In (2.127), the factor is missing from the denominator.
- Page 192: In Footnote 52 to Section 2.6.3, the exponent should be instead.
- Page 203: In Exercise 2.6.6, a factor of is missing in the error term. Earlier in the eigenfunction equation for , should be .
- Page 206: In Remark 2.6.8, the denominator in the first display should instead be in the numerator, and similarly for (2.169); the denominator two displays afterwards should similarly be .
- Page 212: For the application of Markov’s inequality and through to the next page, all appearances of should be replaced by , and “for at least values of ” should be “for at least values of .
- Page 213: In Exercise 2.7.1, should be , the condition should be , the final bound should be rather than , and should be . The definition of incompressibility should be , with to be chosen later, in the next display should be , and “within … positions” on the next paragraph should be “within … positions”. Finally, in footnote 58, the summation should go up to rather than to in both occurrences.
- Page 214: should be (two ocurrences), and should be in Exercise 2.7.2.
- Page 215: In the last line “Proposition 2.7.3″ should be “Proposition 2.7.3 and (2.172)”, and on the next page, should be (two occurrences).
- Page 251: In Exercise 3.1.11, should be . In (3.12) and the preceding display, should be .