Norm of a doubly-stochastic stationary vector

MediumLinear Algebra Stochastic Processes~6m

A Markov chain on $S = \{1, 2, \dots, 100\}$ has a doubly-stochastic transition matrix (every row and every column sums to $1$ ). Let $\pi$ be its stationary distribution. Compute the Euclidean norm $\lVert \pi \rVert_2$ .

Show hints (2)+

Doubly stochastic $\Rightarrow$ the uniform distribution is stationary. What is $\pi$ ?
$\pi_i=\tfrac1{100}$ , so $\lVert\pi\rVert_2=\sqrt{100\cdot(1/100)^2}=\tfrac1{10}$ .

Answer

Reveal answer →

0.1 (± 0.001)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise free Unlock solutions

Asked at: Citadel, Two Sigma

Norm of a doubly-stochastic stationary vector

Answer

Related questions