p. 20In Exercise 1.1.11(i), “if and only for” should be “if and only if for”.
p. 21In Exercise 1.1.18, in the definition of convexity, $\geq$ should be $\leq$.
p. 46In 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 $1 \leq i \leq n$ rather than $1 \leq i \leq p$.
p. 72All occurrences of $2t/\pi$ on this page should be $\pi t/2$.
p. 183The 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. 225-226U should be U_0 (several occurrences). Also, $\frac{1}{\sqrt{n}U}$ should be $\frac{1}{\sqrt{n}}U_0$ and $\frac{1}{\sqrt{n} U_\varepsilon}$ should be $\frac{1}{\sqrt{n}} U_\varepsilon$.
p. 225Section 2.8.2: right parenthesis should be added after “sufficient decay at infinity.”
p. 228just before (2.179): “g_n” should be “f_n”
p. 231“lets ignore” should be “lets us ignore”
p. 258In the second paragraph, $d \times d$ should be $n \times n$, and $X_n$ should be $X_N$.
p. 6In parts (iii), (iv) of Lemma 1.1.3, “the $\bigwedge_\alpha E_\alpha$” should be “then $\bigwedge_\alpha E_\alpha$“.
p. 16In Example 1.1.9, the Poisson distribution should be classified as having sub-exponential tail rather than being sub-Gaussian.
p. 17In Exercise 1.1.5, $\exp(C k^C)$ should be $k^{Ck}$.
p. 18Exercise 1.1.10 is incorrect as stated. Replace the second sentence with “Show that there exists a random variable $Y$ (on the sample space $R$) taking values in $R$, such that $X$ is equal almost surely to an extension of $Y$ (to the sample space $\Omega$), and $X'$ is equal almost surely to an extension of $Y$ (to the sample space $\Omega'$).
p. 22In Exercise 1.1.18(ii), the requirement that the $X_i$ take values in $[0,+\infty]$ should be dropped.
p. 29In Definition 1.1.23, $y$ should lie in $R'$ rather than $R$.
p. 32In Definition 1.1.29, Remark 1.1.30, and Exercise 1.1.25, “$\sigma$-compact” should be “$\sigma$-compact and locally compact”.
p. 37After (1.49), “uniform lower bound” should be “uniform upper bound”, and after the second line of the following display, $|x| > \sqrt{n}$ should be $x > \sqrt{n}$.
p. 41In the proof of Theorem 1.3.1, $\lambda v^* v$ should strictly speaking be $\lambda(v^*v-1)$ (though it makes no difference to the remainder of the argument).
p. 41In Exercise 1.3.1, $u_j(A)^* u_j(A)$ should be $u_j(A) u_j(A)^*$.
p. 45“But, from (1.57)” should be “But, from (1.58)”.
p. 49After (1.72), $\dot u_i^*u_i=0$ should be $\hbox{Re} \dot u_i^* u_i$, and “orthogonal” should be “orthogonal (using the real part of the inner product)”.
p. 51In Section 1.3.6, the role of rows and columns should be reversed in “at least as many rows as columns”.
p. 53In Exercise 1.3.22 (vii), (viii), the eigenvalues $\lambda_i$ should be replaced by singular values $\sigma_i$.
p. 60?: Just before (2.8), $\sqrt{nk}$ should be $\sqrt{k}$.
p. 61In the proof of Theorem 2.1.3, $X$ should be $X_i$ throughout (three occurrences), and ${\bf E} \exp( t S_n) = \exp( O( t^2 \sigma^2 ) )$ should be ${\bf E} \exp( t S_n) \leq \exp( O( t^2 \sigma^2 ) )$. Also, the reference to (2.9) here may be replaced by (2.10). In the second last line of the proof of Lemma 2.1.2, a closing parenthesis is missing.
p. 68In the last display of Proposition 2.1.9, $2^{-m-1}$ should be $\frac{1}{100(m+1)^2}$. The definitions of $X_{i,0}$ and $X_{i,m}$ are missing absolute value signs (they should be $X_{i,0} := X_i {\bf I}(|X_i| \leq 1)$ and $X_{i,m} := X_i {\bf I}(2^{m-1} < |X_i| \leq 2^m )$ respectively). Also, $2^{-m-1} A$ should be $\frac{A}{100(m+1)^2}$.
p. 69In Theorem 2.1.10, $x_j \in X_j$ should be $x_j \in R_j$. In (2.15), $\sigma^2$ should be $\sigma$.
p. 70The footnote “Note that we must have $K \leq 1$…” should read “Note that we should take $K \geq 1$ if we wish to allow the variance to actually be able to attain the value $1$“. The condition $\lambda \leq c\sqrt{n}/\sqrt{K}$ after (2.8) sohuld be $\lambda \leq c \sqrt{n}/K$.
p. 74In the proof of Lemma 2.1.14, $X-A$ should be $A-X$ (two times).
p. 74In the proof of Lemma 2.1.15, $U_B(X') \times \{1\}$ should be $(U_B(X') \backslash U_{A_{X_n}}(X') \times \{1\}$, and $(\lambda t + (1-\lambda)u, 1-\lambda)$ should be “one of $(\lambda t + (1-\lambda)u, 1-\lambda)$ or $(\lambda t + (1-\lambda)u, 0)$“.
p. 76In 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 $X_n$.
p. 81In Remark 2.2.2, “central limit” should be “central limit theorem”
p. ?In Lemma 2.3.1, $\exp(-CAn)$ should be $-\exp(CA^2 n)$.
In Section 2.4: all references to the “circular law” should be to the “semi-circular law”.
p. 88At and just before (2.4.1), $1+|t|$ should be $|t|$. (Also to avoid having to deal with distributions, one should temporarily truncate $1_{(-\infty,a]}$ to, say, $1_{[-M,a]}$ and then let $M$ go to infinity at the end of the argument.) In the display after (2.40), $\hat \eta(t/\varepsilon)$ should be $\hat \eta(\varepsilon t)$. Just before the last display in the proof of Theorem 2.2.8, $|t| \leq c \varepsilon$ should be $|t| \leq c/\varepsilon$.
p. 90In Theorem 2.2.9(i), k should range in 1,2,3,… rather than 0,1,2,… .
p. 95In the first display of the proof of Theorem 2.2.11, $o(1)$ should be $O( \frac{1}{\sqrt{n}} {\bf E} |X|^3 ) \sup_{x \in R} |\phi'''(x)|$.
p. 97Near the end of Section 2.2.5: [TaVuKr2010] should be [TaVu2009b].
p. ?In remark 2.2.12, the discussion on the four moment theorem can be deleted (I never did end up incorporating this material into the text).
p. 98In the proof of Theorem 2.2.13, $\phi$ should be assumed to be Lipschitz and not just continuous.
p. 99In the final display, every term should have an expectation symbol ${\bf E}$ attached to it.
p. 107After (2.58), ${\bf C}^d$ should be ${\bf C}^n$ (two occurrences).
p. 113Before (2.62), the $\bigvee_{1 \leq i < j \leq n}$ symbol should be $\bigwedge_{1 \leq i < j \leq n}$.
p. 114In Proposition 2.3.10, $M \|M\|_{op}$ should be ${\bf M} \|M\|_{op}$ (two occurrences).
p. 117In item (ii) i the list after (2.69), the condition $i_1 \neq i_2$ should be added.
p. 126second line: the $o(1)$ error term needs to be improved to $O(k^2/n)$.
p. 127In the proof of Lemma 2.3.22, the first arrival can be either a fresh leg or a high multiplicity edge, not simply a fresh leg as stated in the text. However, this does not affect the rest of the argument.
p. 128For each non-innovative leg, one also needs to record a leg that had already departed from the vertex that one is revisiting; this increases the total combinatorial cost here from $k^m$ to $k^{2m}$ (and the first display should be similarly adjusted). However, the rest of the argument remains unchanged. In the last display and the first display of the next page, $\max(j+1,k/2)$ should be $\min(j+1,k/2)$.
p. 130The statement “(2.76) holds” should read “(2.76) fails”.
p. ?In the paragraph before Remark 2.4.1, it should be stated that $\mathrm{Pr}({\bf R})$ is equipped with the vague topology, and can be viewed as a measurable subset of the compact space $\mathrm{Pr}({\bf R} \cup \{\infty\})$ of probability measures on the compactification ${\bf R} \cup \{\infty\}$.
p. ?In the definition of the Stieltjes transform before (2.90), $x-z$ should be $z-x$.
p. 157In the discussion of classical independence in Section 2.5, “all of ${\bf E} f(X), {\bf E} g(Y)$ vanishes” should be “${\bf E} f(X), {\bf E} g(Y)$ both vanish”.
p. 170Before Exercise 2.5.10, the constraint $X \in L^\infty(\tau)$ should be $X \in {\mathcal A} \cap L^\infty(\tau)$.
p. 174In Exercise 2.5.15, the additional hypothesis that X and Y are self-adjoint should be added. In Exercise 2.5.16, add “Show more generally that $P(U_1,U_1^*)$ and $Q(U_2,U_2^*)$ are freely independent for any polynomials $P,Q$.
p. 175In the second display, an extra right parenthesis should be added to the left-hand side.
p. 176In the proof of Lemma 2.5.20, $X_i \in {\mathcal A}_i$ should be $X_i \in {\mathcal A}_i^0$. Also, $\tau(X_i Y_{i_1})$ should be $\tau_i(X_i Y_{i_1})$.
p. 181The formulae for $\tau(X^k)$ in Exercises 2.5.20 and Exercises 2.5.21 should be swapped with each other. Also, the formula for the third cumulant $\kappa_3(X)$ is incorrect; this quantity is in fact equal to the third free cumulant $C_3(X)$ (but $\kappa_4(X)$ and $C_4(X)$ are not equal in general).
p. 183In (2.127), the factor $1! \ldots (n-1)!$ is missing from the denominator.
p. 184In the paragraph before (2.128), “eigenvalues of $M$” should be “eigenvalues of $M_n$“.
p. 187-188The derivation of the Ginibre formula requires modification, because the claim that the space of upper triangular matrices is preserved with respect to conjugation by permutation matrices is incorrect. Instead, the given data $G$ needs to be replaced by a pair consisting of the random matrix $G$, together with a random enumeration $\lambda_1,\ldots,\lambda_n$ of the eigenvalues of $G$, and the factorisation $G = U T U^{-1}$ is then subjected to the constraint that $T$ has diagonal entries $\lambda_1,\ldots,\lambda_n$ in that order. (To put it another way, one works in an n!-fold cover of the space of matrices with simple spectrum.) One then performs the analysis in the text, with the enumeration of the eigenvalues of a perturbation of $T_0$ understood to be the one associated with the diagonal entries of $T_0$. (Details may be found at the associated blog entry for this section.)
p. 189In the second paragraph, $\varepsilon^{n^2-n}$ should be $(1+o(1)) \varepsilon^{n^2-n}$.
p. 191In the last line in the paragraph after (2.137), $\frac{1}{|\lambda_i-\lambda_j}$ should be $\log \frac{1}{|\lambda_i - \lambda_j|}$.
p. 192In Footnote 52 to Section 2.6.3, the exponent $2$ should be $1/2$ instead.
p. 199In (2.161), $(-1)^{(n+1)/2}$ should be $(-1)^{(n-1)/2}$.
p. 200In the definition of $\tilde \phi_m$, the first factor of $\sqrt{n}$ should be $n^{1/4}$. In the eigenfunction equation for $\tilde \phi_m$, $L_{1/\sqrt{n}}$ should be $L_{1/n}$.
p. 201In (2.162), $\frac{1}{n}$ should be $\frac{1}{n^{1/4}}$.
p. 203In Exercise 2.6.6, a factor of $n^{-1/2}$ is missing in the $O()$ error term, and $|a|^2(x) + |b|^2(x)$ should be $4 a(0) b(0)$. In the penultimate display, $n^{(n+1)/2}$ should be $n^{\frac{n}{2} + \frac{1}{4}}$.
p. 206In Remark 2.6.8, the $n^{1/6}$ denominator in the first display should instead be in the numerator, and similarly for (2.169); the $n^{-1/6}$ denominator two displays afterwards should similarly be $n^{1/6}$.
p. 212For the application of Markov’s inequality and through to the next page, all appearances of $8$ should be replaced by $8/\delta$, and “for at least $n/2$ values of $j$” should be “for at least $(1-\delta/2)n$ values of $j$. Any appearance of $\mathbf{C}^p$ should instead be $\mathbf{R}^p$.
p. 213In Exercise 2.7.1, $r/\|x\|^2$ should be $r/\|x\|$, the condition $\sum_{j: |x_j| \leq \varepsilon^{100}} |x_j|^2 \geq \varepsilon^{10}$ should be $\sum_{j: |x_j| \leq \varepsilon} |x_j|^2 \geq \eta$, the final bound should be $\ll_{\eta,\delta} \varepsilon$ rather than $\ll \varepsilon$, and $|x_j| > 1/2$ should be $|x_j| > \varepsilon$. The definition of incompressibility should be $\sum_{j: |x_j| \leq \varepsilon} |x_j|^2 \geq \eta$, with $\eta>0$ to be chosen later, in the next display $O(\varepsilon)^n$ should be $(O_{\eta,\delta}(\varepsilon))^{(1-\delta/2)n}$, and “within $\varepsilon$ … $\varepsilon^{-200}$ positions” on the next paragraph should be “within $\eta$ … $\varepsilon^{-2}$ positions”. Finally, in footnote 58, the summation should go up to $n$ rather than to $3$ in both occurrences. Just before this exercise, $x_i$ and $\xi_i$ should go up to $p$ rather than $n$ (with some corresponding changes within the exercise).
p. 214$n^{O_\varepsilon(1)}$ should be $n^{O_{\varepsilon,\eta}(1)}$ (two occurrences), and $2C \varepsilon \sqrt{n}$ should be $2C \eta \sqrt{n}$ in Exercise 2.7.2.
p. 215In the last line “Proposition 2.7.3” should be “Proposition 2.7.3 and (2.172)”, and on the next page, $O(\sqrt{k})^{-(n-k)}$ should be $\hbox{min}( 1/2, O(k^{-1/2}) )^{n-k}$ (two occurrences). Somewhat previously, the entropy cost of $\lfloor \varepsilon n \rfloor \binom{n}{k}$ should just be $\binom{n}{k}$.
p. 216In the treatment of the incompressible case, every row $X_k$ shuold be replaced instead with the corresponding column $Y_k$.
p. 217In Exercise 2.7.3, $\hbox{dist}(X_i,V_i)^2$ should be $\hbox{dist}(X_i,V_i)^{-2}$. “$\sum_{i=1}^n \sigma_i(M)^{-2} = O(1)$” should be “$\sum_{i=1}^n \sigma_i(M)^{-2}$ is comparable to $1$.” “eigenvalues $\sigma_i(M)$” should be “singular values $\sigma_i(M)"$.
p. 218After the first complete sentence, add “This of course contains the event that $\|Mx\| \leq \lambda/\sqrt{n}$.”
p. 220In Section 2.7.5, all occurrences of $\sqrt{n} \sigma_n(M)$ should be $n \sigma_n(M)^2$.
p. 223in Theorem 2.8.1: add “in the vague topology” after “converges”.
p. 225In Section 2.8.2, all integrals should be over ${\bf C}$ rather than ${\bf R}$. In Exercise 2.8.3, it should be noted that $\frac{1}{w-z}$ is interpreted in a principal value sense.
p. 226-227All occurrences of $\frac{1}{\sqrt{n} M_n}$ should be $\frac{1}{\sqrt{n}} M_n$.
p. 228All occurrences of “operator norm” should be “spectral radius”.
p. ?In Theorem 2.8.3, add the hypotheses that $\|\frac{1}{\sqrt{n}} M_n\|_{op} = O(1)$ almost surely, and that $\mu$ is compactl supported.
p. 237In Proposition 3.1.5, “same distribution as $\mu$” should be “same distribution as $(X_t)_{t \in \Sigma}$. Similarly in Proposition 3.1.16.
p. 246The statement and proof of Theorem 3.1.16 have a number of issues. A corrected version can be found at this blog post.
p. 251In Exercise 3.1.11, $t^{-n^2/2}$ should be $t^{-n/2}$. In (3.12) and the preceding display, $n!$ should be $(n-1)!$.
p. ?In the last part of Section 2, the threshold $\lambda$ for $X_1 + \dots + X_n$ should be $\lambda \sigma$, and the factors of $e^{-t\lambda}$ should similarly be $e^{-t\lambda\sigma}$.
p. 267In the display after “Hermite polynomial”, $\frac{d}{dx^2}$ should be $\frac{d^n}{dx^n}$.
p. 269In Section 3.4.2, the expansion into Haar coefficients of $\sum_j \frac{x_j^2}{2}$ should instead be of $\sum_j x_j^2$.
Contributors
Thanks to all those who have contributed corrections. Corrections received on or before 2026-07-09 were reported by the readers listed below over the years; individual per-erratum attributions for these legacy entries were not preserved in migration.