Markov chains in Monte Carlo

The chain of events is called a Markov chain if the conditional probability of a specific outcome En+, provided a sequence of given previous outcomes Ei,E2,---,En,iS 

This means that for a Markov chain the probability of each outcome only depends on the immediately previous event. We also call the Markov chain a single step transition probability chain. 

Consequently, the joint probability of a certain sequence of events is 

Metropolis Monte Carlo algorithms generate a Markov chain of states in phase space. That is, each new state generated is not independent of the previously generated ones. Instead, the new state depends on the immediately preceding state. 

The method has one important condition the outcome of a trial belongs to a finite set of outcomes. In other words, there is a finite number, M, of phase state points LKi, Lj f corresponding to a 

---