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...Mathd markov chains mariacameron contents discrete time evolution of the probability distribution communicating classes and irreducibility hitting times absorption probabilities solving recurrence relationships transience invariant distributions measures reversal detailed balance chain monte carlo methods metropolis hastings algorithms ising model mcmcforcryptography continuous right random processes exponential jump holding class structure convergence to equilibrium for transition path theory settings reactive trajectories forward backward committors current eective rate reaction pathways simplications reversible sampling no detour metastability more on spectral analysis eigencurrents eigenstructure networks with interpretation eigenvalues eigenvectors versus tpt references think about following problem example gambler s ruin imagine a who has initially at each moment t can play if he it win one p or lose q runs out money is ruined cannot anymore what that will be thegamblingprocessde...