Kemeny Random-Target Hitting

Kemeny's constant is an intriguing invariant of finite, irreducible Markov chains. It reveals that the expected time to hit a randomly chosen target state (chosen according to the chain's stationary distribution) is the same regardless of the starting state.

Experiment

You can test the start-state invariance in the interactive model:

Check out the model and verify the results yourself.

1. Open the Kemeny Random-Target Hitting module.
2. Set the Chain control to Complete and Move probability to 0.5.
3. Observe that the K from zero, K from one, and K from two result cards all display exactly 4.0.
4. Change the Start control to a different state (e.g., 1). Notice that the Selected hitting time changes depending on the Target, but the Kemeny constants remain exactly 4.0.