Link to the Errata page.

**Chapter 1**, page 10-11, Exercise 1.6:

[…] interacting through the van der Waals force (equation (1.11) […]

**NOTE:**Equation (1.11) is the expression of the van der Waals*potential*. You need to use a force. Therefore, you should derive the van der Waals*force*from equation (1.11) by using the standard definition of force (i.e., the force is minus the gradient of the potential) stated in equation (1.6).**Chapter 2**, page 3, Exercise 2.1:

**a.**[…] How many steps are necessary to reach the equilibrium distribution?

**NOTE:**Strictly speaking, you will never (or hardly ever) obtain the*exact*theoretical equilibrium distribution P_{theo}(x) from a realization with a finite number of steps. However, you can measure how close the*numerical*distribution P_{num}(x) (the one you obtain from the simulated trajectory with a finite number of steps) is from the equilibrium distribution: for example, you can define the distance as (∑_{x}(P_{num}(x)-P_{theo}(x))^{2})^{0.5}.

Therefore: (1) choose a value of the distance*d*_{ref}below which you consider to be close enough to the equilibrium; (2) determine the number of steps above which your trajectory shows to be enough close to the equilibrium.

Of course, the smaller*d*_{ref}, the larger the number of steps you need to consider the numerical trajectory close to the equilibrium.**Chapter 2**, page 3, Exercise 2.1:

**b.**[…] their effect on the transition frequency between states […].

**NOTE 1:***transition frequency between states*etc means, transition from*Left to Right*or from*Right to Left*.

Even if there is no direct transition from Left to Right or viceversa, as the system must pass through the Middle state, the attention is directed to the following question: How often the system changes from being in the Left state to reach the Right state? And viceversa?

Measure this, for example, by segmenting your trajectory appropriately. Example: starting from the initial position on the Left, and ending the first segment on the first occasion the system finds itself to the Right. At this point, start another segment from the first successive occasion the system is again in the Left state, and end the segment when it reaches the Right state. Continue till the points in the trajectory are exhausted. Each of the segment has a “length” in number of steps. The frequency can be measured as the inverse of the average number of steps of the segments. Repeat for the transition Right to Left to estimate the transition frequency from Right to Left.*[Reflect: do you expect these two frequency to be similar?]*

**b.**[…] Does it affect also the time it takes the system to reach the equilibrium distribution?

**NOTE 2:***The time it takes the system*etc means, here, the number of steps. However, as it becomes clear from the numerical experiment, this quantity slightly depends on the specific pseudo-random sequence used to determine the trajectory.**Chapter 3**, page 3, Exercise 3.1.

**NOTE:**How do you propagate the fire in practice?

When the initial cell is burning, you expand the fire by checking the cell direction upwards, leftwards, downwards, and rightwards. Then you re-iterate the process and stop when you find either empty cells or cells with burned tree.**Chapter 3**, page 4, Exercise 3.3.

**NOTE:**The final part of the hint, the one beginning with*You might execute this exercise*etc is**very important**to implement the numerical generation of random numbers with the wanted power-law probability distribution.