# Tag Info

## Hot answers tagged markov-chains

### "Surprising" examples of Markov chains

I could go back to Markov himself, who in 1913 applied the concept of a Markov chain to sequences of vowels and consonants in Alexander Pushkin's poem Eugene Onegin. In good approximation, the ...
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### "Surprising" examples of Markov chains

I believe that if $(X_n)$ is a biased simple random walk on $[-N,N]$, then $|X_n|$ is a Markov chain.
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### "Surprising" examples of Markov chains

Consider the Metropolis-Hastings algorithm which is an MCMC method, i.e., a general purpose Monte Carlo method for producing samples from a given probability distribution. The method works by ...
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### "Surprising" examples of Markov chains

One example I enjoy is that if you add a list of numbers, the carries form a markov chain Carries, Shuffling and An Amazing Matrix Carries, shuffling, and symmetric functions If $n$ integers in base ...
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### Does every (generalized?) Markov chain admit transition probabilities?

Under mild conditions on the state space $(S, \mathcal{S})$, it is true. For instance, it is sufficient that it be standard Borel. In that case, each $\xi_k$ admits a regular conditional ...
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### Frequency of visiting states in Markov chains

An ergodic finite Markov chain satisfies a $0-1$ law. If it is possible (i.e. probability $> 0$) to have more than $b$ visits to state $m$ in a time interval of length $a$, then with probability $1$...
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### How to sample a uniform random polyomino?

Here is an approach to estimating parameters of uniformly random polyominoes of $n$ squares without generating random ones uniformly. First define a rooted tree whose root is the single square and ...
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### Ergodicity of the product Markov chain

No - this is not true. The minimal example is provided by the deterministic Markov chain with two states (so that the state space is $\mathbb Z_2=\{0,1\}$) with the deterministic transitions \$x\mapsto ...
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### Markov Process, Markov Chain

These terms (Markov chain / Markov process) seems to be mostly interchangeable, especially if one cares to specify whether the time is discrete or continuous. I would prefer "chain" to mean discrete ...
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