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2020 A solvable class of renewal processes
Nathanaël Enriquez, Nathan Noiry
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP348


When the distribution of the inter-arrival times of a renewal process is a mixture of geometric laws, we prove that the renewal function of the process is given by the moments of a probability measure which is explicitly related to the mixture distribution. We also present an analogous result in the continuous case when the inter-arrival law is a mixture of exponential laws. We then observe that the above discrete class of renewal processes provides a solvable family of random polymers. Namely, we obtain an exact representation of the partition function of polymers pinned at sites of the aforementioned renewal processes. In the particular case where the mixture measure is a generalized Arcsine law, the computations can be explicitly handled.


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Nathanaël Enriquez. Nathan Noiry. "A solvable class of renewal processes." Electron. Commun. Probab. 25 1 - 14, 2020.


Received: 17 April 2020; Accepted: 3 September 2020; Published: 2020
First available in Project Euclid: 24 September 2020

MathSciNet: MR4158229
Digital Object Identifier: 10.1214/20-ECP348

Primary: 30D35, 60K05, 82D60


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