 # Complexity Explorer Santa Few Institute ## Random Walks

• Introduction
• Brownian Motion
• Types of Random Walks
• Root Mean Square Displacement
• Role of the Spatial Dimension
• Part I
• Part II
• Part III
• Part IV
• A poor person's fluctuation dissipation relation
• Part I
• Part II
• Part III
• First Passage Phenomena
• Part I
• Part II
• Final Remarks
• Homework Solutions

#### 4.1 Part I » Quiz Solutions

4.1 Q1

Consider a 10-step symmetric nearest-neighbor random walk in one dimension.

(a) What is the probability that the walk is at x=10?   4.1 Q2

Consider a 10-step symmetric nearest-neighbor random walk in one dimension.

(b) What is the (approximate) probability that the walk is at the origin?   4.1 Q3

(Harder) Consider a 6-step nearest-neighbor random walk in one dimension in which the
walk hops to the right with probability 2/3 and hops to the left with
probability 1/3.

(a) What is the probability that the walk is at x=6?   4.1 Q4

(Harder) Consider a 6-step nearest-neighbor random walk in one dimension in which the
walk hops to the right with probability 2/3 and hops to the left with
probability 1/3.

(b) What is the (approximate) probability that the walk is at the origin?   