Proves exponential decay of pair correlations in 1D point processes via a Markov renewal theorem with exponential rate, under Markovian spacings, geometric ergodicity, and exponential moments, with applications to Gibbs processes and harmonic chains.
Nummelin,A splitting technique for Harris recurrent Markov chains, Probab
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Markov Renewal Theory for Transfer Operators and Point Processes on the Line
Proves exponential decay of pair correlations in 1D point processes via a Markov renewal theorem with exponential rate, under Markovian spacings, geometric ergodicity, and exponential moments, with applications to Gibbs processes and harmonic chains.