# Order of magnitude time-reversible Markov chains and characterization of clustering processes

@article{Joshi2011OrderOM, title={Order of magnitude time-reversible Markov chains and characterization of clustering processes}, author={Badal Joshi}, journal={arXiv: Probability}, year={2011} }

We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge of order of magnitude of the transition probabilities. For an irreducible, OM-reversible Markov chain on a finite state space, we prove that the stationary distribution satisfies order of magnitude detailed balance (analog of detailed balance in reversible… Expand

#### References

SHOWING 1-10 OF 31 REFERENCES

Mean Passage Times and Nearly Uncoupled Markov Chains

- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 1992

The chemical basis of morphogenesis

- Mathematics
- Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
- 1952

Dynamics of Cdc42 network embodies a Turing‐type mechanism of yeast cell polarity

- Biology, Medicine
- FEBS letters
- 2008