Markov Chain Mixing Rate

Problem

Return the mixing rate of a 2x2 row-stochastic matrix P: the absolute value of its second eigenvalue.

One eigenvalue is always 1, so the second is trace(P) - 1 and the mixing rate is |trace(P) - 1|.

Hint

A smaller mixing rate means faster convergence to the stationary distribution.

case 1

in: [[[0.5,0.5],[1,0]]]

expected: 0.5

case 2

in: [[[0.9,0.1],[0.3,0.7]]]

expected: 0.6

case 3

in: [[[1,0],[0,1]]]

expected: 1

case 4

in: [[[0.5,0.5],[0.5,0.5]]]

expected: 0

Starter codePython

def markov_mixing_rate(P):
    # Your code here
    pass

4 test cases · run your code against them in the editor