List of Errata

(updated January 9, 2007)

Chapter 1:

1. Page 2. The second paragraph should read: ``To make these questions precise and then answer them, note that the price performs a symmetric random walk in $n$, where $n=N_--N_+$ is the difference in the number of ``down'' and ``up'' days, $N_-$ and $N_+$, respectively.
   I thank Ronny Straube for pointing out this error.

2. Page 5. The second sentence of Sec. 1.2 should read: An important starting fact is that the survival probability $S(t)$ in an absorbing domain is closely related to the time integral of the first-passage probability up to time $t$ over the spatial extent of the boundary (see Eq. (1.5.7)).

3. Page 8. The integral in Eq. (1.3.5) is over the range $-\pi\leq k\leq \pi$. This is not a contour integral.

4. Page 9. In Eq. (1.3.8), the factor $Np$ in the exponential should be $N(p-q)$.
   I thank David Waxman for pointing out these three errors.

5. Page 9. The second line of the un-numbered formula after Eq. (1.3.8) should read: $\sim e^{ik\langle x\rangle-{1\over 2}k^2(\langle x^2\rangle -\langle x\rangle^2)},\quad k\to 0$.

6. Page 9. Eq. (1.3.9) should read: $P(x,N)\to {1\over \sqrt{2\pi N(\langle x^2\rangle-\langle x\rangle^2)}}\,\, e^{-(x-\langle x\rangle)^2/[2N(\langle x^2\rangle-\langle x\rangle^2)]}$.
   I thank Paul Krapivsky for pointing out these two errors.

7. Page 10. In Eq. (1.3.11), the denominator inside the square brackets should be $2zq$ for $x>0$ and $2zp$ for $x<0$.
   I thank David Waxman for pointing out this error.

8. Page 11. In Eq. (1.3.13), the left-hand side should read $\frac{\partial P(n,t)}{\partial t}$.

9. Page 22. In Eq. (1.5.6), the factor $(1-R)$ should read $(1-{\cal R})$.

10. Page 31. In Eq. (1.6.22), the argument on the left-hand side should be $\vec r$, not $\vec r'$.

Chapter 2:

1. Page 47. The factor in the second of Eqs. (2.2.16) should be $(1-u_0^2)$ not $(1-u_0)^2$.

2. Page 57. The signs of the $v$ and $D$ terms are *not* opposite to the sense of the corresponding terms in the convection-diffusion equation.

3. Page 63. Just above (2.2.23), the reference is to (1.6.27) not (1.6.29).

Chapter 3:

1. Page 66. In Eq. (3.2.6) there should be no $t$ in the factor before the integral.

2. Page 83. In Eq. (3.2.4) the derivative should be with respect to $x$ not $t$.
   I thank Carl Gold for pointing out this error.

3. Page 84. In Eq. (3.2.6) there is no factor of $t$ in the square root.
   I thank Robin Groenevelt for pointing out this error.

4. Page 87. In Eq. (3.2.12) the prefactor in the second term should be $e^{-vx_0/D}$. Similarly, in the first and also the third line below this equation the factor should read $e^{-vx_0/D}$.

5. Page 88. Replace $x$ by $x_0$ in the line after (3.2.14) and in the first line of (3.2.15). Also, the fontsize for the first factor of $P\!e$ in the 3rd line of this formula is the wrong size.

6. Page 89. The second half of of Eq. (3.2.16) is incorrect. The correct result is $\left({x_0\over\sqrt{Dt}}\right)^3{1\over\sqrt{4\pi}}{1\over{P\!e}^2} \,e^{-P\!e^2\,Dt/x_0^2}=\sqrt{4\over\pi}{x_0\sqrt{Dt}\over (vt)^2}\, e^{-v^2t/4D}$
   I thank David Mukamel for pointing out the above two errors.

7. Page 93. The prefactor in Eq. (3.3.1) should be $1\over{\sqrt{4Ds}}$.

8. Page 99. In the last two lines of Eq. (3.4.4), the factor in the denominator should be $2(t-1)$ not $2t-1$.

9. Page 108. Add the word ``with'' in the $9^{\rm th}$ line. It should read ``$\ldots$ returned to site 1 with probability $r\ldots$''. I thank Ronny Straube for pointing out this error.

Chapter 4:

1. Page 123. Sec. 4.3.2, third line: ``Flyvbjerg'', not ``Flyvbjery''.

2. Page 130. The last term should read ${1\over 2}(r_{\rm in}+r_{\rm out}){\partial^2 P\over \partial n^2}$.
   I thank Paul Krapivsky for pointing out this error.

3. Page 151. The sign of the third term on the right-had side of Eq. (4.6.1) should be plus, not minus.
   I thank Alex Petersen for pointing out this error.

4. Page 152. Remove the word ``a'' four lines after Eq. (4.6.6).

5. Page 162. In the line after Eq. (6.2.3b), the factor should read $(a/r_0)^{d-2}$.

6. Page 166. The double subscript $y_{y1}$ should simply be $y_1$.
   I thank Robin Groenevelt for pointing out this error.

Chapter 7:

1. Page 236. In the first sentence of the third paragraph, the phrase ``We thus define $c(r,\theta,t=0)\ldots$'' is missing an equal sign.

2. Page 243. In Eq. (7.4.3), the fraction $\frac{1}{2\pi D}$ should be replaced by $D$.
   I thank Robin Groenevelt for pointing out these two errors.

Chapter 6:

1. Page 209. The result in the second of Eq. (6.2.2) actually gives ${\cal E}_-(r)$. The correct result is:
   $$\begin{eqnarray*} {\cal E}_+(r)=\frac{\ln(r/R_-)}{\ln(R_+/R_-)}. \end{eqnarray*}$$
   
   
   I thank Ronny Straube for pointing out this error.

2. Pages 226-227. In the first formula in subsection 6.5.2.2 and in the first un-numbered formula after Eq. (6.5.6), the prefactor should be $\sqrt{\frac{D}{s}}$ rather than $\frac{D}{s}$.
   I thank Ronny Straube for pointing out these two errors.

Chapter 8:

1. Page 261. In Eq. (8.2.10) the factor $\ln w$ in the exponential should read $\ln q$.

2. Page 266. The expression for $\Theta_{\rm end}$ should read:
   
   $$\Theta_{\rm end}=\pi -\cos^{-1}{D_3\over\sqrt{(D_1+D_3)(D_2+D_3)}},$$
   
   
   while the final expression for $\beta_{\rm end}$ should read
   
   $$\left[2-{2\over\pi}\cos^{-1}{D_3\over\sqrt{(D_1+D_3)(D_2+D_3)}}\right]^{-1}.$$
   
   
   
   I thank Alan Bray for pointing out this error.

3. Page 269. In figure 8.6(a) the labels $1=3$ and $2=3$ should be transposed.

4. Page 284. In Eq. (8.4.24), the expression for $c_k(t)$ should have a $t^{-3/2}$ time dependence in the prefactor, not $t^{-1/2}$.
   I thank Pu Chen for pointing out this error.