@unpublished{20572,
  abstract     = {We present an elementary non-recursive formula for the multivariate moments
of the Dirichlet distribution on the standard simplex, in terms of the pattern
inventory of the moments' exponents. We obtain analog formulas for the
multivariate moments of the Dirichlet-Ferguson and Gamma measures. We further
introduce a polychromatic analogue of Ewens sampling formula on colored integer
partitions, discuss its relation with suitable extensions of Hoppe's urn model
and of the Chinese restaurant process, and prove that it satisfies an adapted
notion of consistency in the sense of Kingman.},
  author       = {Dello Schiavo, Lorenzo and Quattrocchi, Filippo},
  booktitle    = {arXiv},
  keywords     = {Dirichlet distribution, Ewens sampling formula, Hoppe urn model, colored partitions},
  title        = {{Multivariate Dirichlet moments and a polychromatic Ewens sampling formula}},
  doi          = {10.48550/arXiv.2309.11292},
  year         = {2023},
}

@inproceedings{10004,
  abstract     = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.},
  author       = {Chatterjee, Krishnendu and Doyen, Laurent},
  booktitle    = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science},
  isbn         = {978-1-6654-4896-3},
  issn         = {1043-6871},
  keywords     = {Computer science, Heuristic algorithms, Memory management, Automata, Markov processes, Probability distribution, Complexity theory},
  location     = {Rome, Italy},
  pages        = {1--13},
  publisher    = {Institute of Electrical and Electronics Engineers},
  title        = {{Stochastic processes with expected stopping time}},
  doi          = {10.1109/LICS52264.2021.9470595},
  year         = {2021},
}

@article{11685,
  abstract     = {We consider the problem of sampling URLs uniformly at random from the Web. A tool for sampling URLs uniformly can be used to estimate various properties of Web pages, such as the fraction of pages in various Internet domains or written in various languages. Moreover, uniform URL sampling can be used to determine the sizes of various search engines relative to the entire Web. In this paper, we consider sampling approaches based on random walks of the Web graph. In particular, we suggest ways of improving sampling based on random walks to make the samples closer to uniform. We suggest a natural test bed based on random graphs for testing the effectiveness of our procedures. We then use our sampling approach to estimate the distribution of pages over various Internet domains and to estimate the coverage of various search engine indexes.},
  author       = {Henzinger, Monika H and Heydon, Allan and Mitzenmacher, Michael and Najork, Marc},
  issn         = {1389-1286},
  journal      = {Computer Networks},
  keywords     = {URL sampling, Random walks, Internet domain distribution, Search engine size},
  number       = {1-6},
  pages        = {295--308},
  publisher    = {Elsevier},
  title        = {{On near-uniform URL sampling}},
  doi          = {10.1016/s1389-1286(00)00055-4},
  volume       = {33},
  year         = {2000},
}

@inbook{4317,
  author       = {Barton, Nicholas H},
  booktitle    = {Analytical biogeography: An integrated approach to the study of animal and plant distributions},
  editor       = {Myers, Alan and Giller, Paul},
  isbn         = {978-0-412-40050-6},
  issn         = {978-94-009-0435-4},
  keywords     = {biogeography, biology, complexity, distribution, evolution, geology},
  pages        = {185 -- 218},
  publisher    = {Springer},
  title        = {{Speciation}},
  doi          = {10.1007/978-94-009-0435-4},
  year         = {1988},
}