Exponential convergence of products of stochastic matrices
By J. Anthonisse, Henk C. Tijms. 1977
Abstract This paper considers a finite set of stochastic matrices of finite order. Conditions are given under which any product of matrices from this set converges to a constant stochastic matrix. Also, it is shown that the convergence is exponentially fast.
Subfields: Probabilistic & Bayesian Methods, Mathematical Optimization
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In Probabilistic & Bayesian Methods
Citations in the corpus
- Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth (2021, background): “Perhaps the convergence to rank one of a path should come as no surprise: each path component contains row-stochastic matrices as a result of the softmax attention, and [AT77] showed the exponential convergence of products of stochastic matrices to rank one.”