Post-class edits

Advanced/Random Walks/parts/0 random.tex

@@ -6,8 +6,8 @@ We would like to compute the probability of our particle stopping at node $A$. \
 
 \vspace{2mm}
 
-In other words, we want a function $P(n): N \to [0, 1]$ that returns the probability that our particle stops at $A$,
-where $N$ is the set of nodes in $G$.
+In other words, we want a function $P: \text{Nodes} \to [0, 1]$ that maps each node of the graph
+to the probability that our particle stops at $A$.
 
 \begin{center}
 \begin{tikzpicture}
@@ -92,11 +92,17 @@ Find $P(x)$ in terms of $P(v_1), P(v_2), ..., P(v_n)$.
 
 
 \problem{}
-How can we use \ref{oneunweighted} to find $P(n)$ for any $n$?
+In general, how do we find $P(n)$ for any node $n$?
 
 \begin{solution}
 	If we write an equation for each node other than $A$ and $B$, we have a system of $|N| - 2$
 	linear equations in $|N| - 2$ variables.
+
+	\vspace{2mm}
+
+	We still need to show that this system is nonsingular, but
+	that's outside the scope of this handout. This could
+	be offered as a bonus problem.
 \end{solution}
 
 \vfill