I wonder if anyone knows a research article that uses the canonical path method (or congestion ratio) to show that a Poincare inequality holds (see the images below)

The canonical path method is a famous way of showing that the Poincare inequality holds (or the spectral gap is positive), which, in turn, implies the exponential ergodicity of the Markov chain. Here is a snapshot of the method and the relative theorem (from page 47 and 48 of Counting and Markov Chains by Mark Jerrum): enter image description here

enter image description here

All the references I have found regarding the canonical path method assume that the relevant Markov chains operate within a finite state space. However, as evident from the above images, I believe this method can still be applied to continuous-time Markov chains on a countable state space. Therefore, I kindly request information on any papers that have utilized the canonical path method for a continuous-time Markov chain on a countable state space

I wonder if anyone knows a research article that uses the canonical path method (or congestion ratio) to show that a Poincare inequality holds (see the images below) for a continuous-time Markov chain on a countable state space.

The canonical path method is a famous way of showing that the Poincare inequality holds (or the spectral gap is positive), which, in turn, implies the exponential ergodicity of the Markov chain. Here is a snapshot of the method and the relative theorem (from page 47 and 48 of Counting and Markov Chains by Mark Jerrum): enter image description here

enter image description here

All the references I have found regarding the canonical path method assume that the relevant Markov chains operate within a finite state space. However, as evident from the above images, I believe this method can still be applied to continuous-time Markov chains on a countable state space. Therefore, I kindly request information on any papers that have utilized the canonical path method for a continuous-time Markov chain on a countable state space

I wonder if anyone knows a research article that uses the canonical path method (or congestion ratio) to show that a Poincare inequality holds (see the images below)

The canonical path method is a famous way of showing that the Poincare inequality holds (or the spectral gap is positive), which, in turn, implies the exponential ergodicity of the Markov chain. Here is a snapshot of the method and the relative theorem (from page 47 and 48 of Counting and Markov Chains by Mark Jerrum): enter image description here

enter image description here

All the references about the canonical path method assumed that Markov chains of interest are on a finite state space. As you can see above, however, I think this method still works for a Markov chain on a countable state space. So, please let us know if you know a paper that used the canonical path method for a continuous-time Markov chain on a countable state space.

I wonder if anyone knows a research article that uses the canonical path method (or congestion ratio) to show that a Poincare inequality holds (see the images below)

The canonical path method is a famous way of showing that the Poincare inequality holds (or the spectral gap is positive), which, in turn, implies the exponential ergodicity of the Markov chain. Here is a snapshot of the method and the relative theorem (from page 47 and 48 of Counting and Markov Chains by Mark Jerrum): enter image description here

enter image description here

All the references I have found regarding the canonical path method assume that the relevant Markov chains operate within a finite state space. However, as evident from the above images, I believe this method can still be applied to continuous-time Markov chains on a countable state space. Therefore, I kindly request information on any papers that have utilized the canonical path method for a continuous-time Markov chain on a countable state space