# On the α-lazy version of Markov chains in estimation and testing problems

arXiv: https://arxiv.org/abs/2105.09536 · HTML: https://mlsanity.com/paper/2105.09536/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 20 May 2021.

## Builds on (most cited first, 4 of 4)

- [Estimating the Mixing Time of Ergodic Markov Chains](https://mlsanity.com/paper/1902.01224/) (2019)
- [On Learning Markov Chains](https://mlsanity.com/paper/1810.11754/) (2018)
- [Minimax Testing of Identity to a Reference Ergodic Markov Chain](https://mlsanity.com/paper/1902.00080/) (2019)
- [Identity testing of reversible Markov chains](https://mlsanity.com/paper/2105.06347/) (2021)

## Built on by (most cited first, 2 of 2)

- [Just Wing It: Near-Optimal Estimation of Missing Mass in a Markovian Sequence](https://mlsanity.com/paper/2404.05819/) (2024)
- [TBP-mHC: full expressivity for manifold-constrained hyper connections through transportation polytopes](https://mlsanity.com/paper/2605.21724/) (2026)

## Abstract (arXiv)

Given access to a single long trajectory generated by an unknown irreducible Markov chain M, we simulate an α-lazy version of M which is ergodic. This enables us to generalize recent results on estimation and identity testing that were stated for ergodic Markov chains in a way that allows fully empirical inference. In particular, our approach shows that the pseudo spectral gap introduced by Paulin [2015] and defined for ergodic Markov chains may be given a meaning already in the case of irreducible but possibly periodic Markov chains.