Publications and Preprints of Dudley Stark

1. "First occurence in pairs of long words: a Penney-ante conjecture of Pevzner" , Combinatorics, Probability & Computing, 4 (1995), 279-285.

2. "Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies" , with Richard Arratia and Simon Tavaré, Annals of Probability, 23 (1995), 1347-1388

3. "A Darboux type theorem for slowly varying functions" , with Boele Braaksma, Journal of Combinatorial Theory, Series A, 77 (1997), 51-66.

4. "Explicit non-zero limits of total variation distance in independent Poisson approximations of logarithmic combinatorial assemblies" , Combinatorics, Probability & Computing, 6 (1997), 87-106.

5. "Total variation asymptotics for independent process approximations of logarithmic multisets and selections" , Random Structures & Algorithms, 11 (1997), 51-80.

6. "Asymptotic enumeration of convex polygons" , with Nicholas Wormald, Journal of Combinatorial Theory, Series A, 80 (1997), 196-217.

7. "The asymptotic number of set partitions with unequal block sizes" , with Arnold Knopfmacher, Andrew M. Odlyzko, Boris Pittel, L. Bruce Richmond, George Szekeres, Nicholas Wormald, Electronic Journal of Combinatorics , 6 R2 (1999), 36 pp.

8. "Total variation asymptotics for refined Poisson process approximations of logarithmic combinatorial assemblies" , Combinatorics, Probability & Computing, 8 (1999), 567-598.

9. "Poissonian behavior of Ising spin systems in an external field" , with Ayalvadi Ganesh, Ben Hambly, Neil O'Connell and Paul Upton, Journal of Statistical Physics, 99 (2000), 613-626.

10. "The characteristic polynomial of a random permutation matrix" , with Ben Hambly, Peter Keevash and Neil O'Connell, Stochastic Processes and Applications, 90 (2000), 335-346.

11. "Compound Poisson approximations of subgraph counts in random graphs" , Random Structures & Algorithms, 18 (2001), 39-60.

12. "Information loss in riffle shuffling" , with Ayalvadi Ganesh and Neil O'Connell, Combinatorics, Probability & Computing, 11 (2002), 79-95.

13. "A prolific construction of strongly regular graphs with the n-e.c. property", with Peter Cameron, Electronic Journal of Combinatorics , 9 R31 (2002), 12 pp.

14. "Information loss in top to random shuffling" , Combinatorics, Probability & Computing, 11 (2002), 607-627.

15. "The vertex degree distribution of random intersection graphs" . Random Structures & Algorithms, 24 (2004), 249-258.

16. "Convergence in distribution for subset counts between random sets" . Electronic Journal of Combinatorics , 11 R59 (2004), 9 pp.

17. "Asymptotic enumeration and logical limit laws for expansive multisets" , with Boris Granovsky, Journal of the London Mathematical Society (2), 73 (2006), 252-272.

18. "Logical limit laws for logarthmic structures" . Mathematical Proceedings of the Cambridge Philosophical Society, 140 (2006), 537-544.

19. "Asymptotic enumeration of incidence matrices" , with Peter Cameron and Thomas Prellberg, Journal of Physics: Conference Series , 42 (2006), 59-70.

20. "The degree of a typical vertex in generalized random intersection graph models" , with Jerzy Jaworski and Michal Karonski, Discrete Mathematics, 306 (2006), 2152-2165.

21. "Asymptotics for incidence matrix classes" , with Peter Cameron and Thomas Prellberg, Electronic Journal of Combinatorics , 13 R85 (2006), 19 pp.

22. "The vertex degree distribution of passive random intersection graph models" , with Jerzy Jaworski, Combinatorics, Probability & Computing, 17 (2008), 549-558.

23. "Meinardus' theorem on weighted partitions: extensions and a probabilistic proof" , with Boris Ganovsky and Michael Erlihson, Advances in Applied Mathematics, 41 (2008), 307-328.

24. "Peak production in an oil depletion model with triangular field profiles" . Journal of Interdisciplinary Mathematics, 11 (2008), 695-706.
    In 1956 M. King Hubbert used curve fitting to predict that the rate of oil production in the U.S.A would peak some time between 1965 and 1970. U.S.A. oil production actually peaked in 1970 and has been declining ever since. This paper analyzes a model of oil depletion with triangular shaped field profiles, giving one of the first theoretical justifications for Hubbert-type curves. Here is a pdf file of the paper. I've written a summary of this paper for The Oil Drum

25. "The limit of the statistic R/P in models of oil discovery and production" . Applied Mathematical Sciences, 3 (2009), 2703-2706.
    This paper shows that the statistic R/P is useless for assessing oil reserves in some models of oil discovery and production. Here is a pdf file of the paper. I've written a summary of this paper for The Oil Drum

26. "Asymptotic enumeration of 2-covers and line graphs" , with Peter Cameron and Thomas Prellberg, Discrete Mathematics, 310 (2010) 230-240.

27. "Random preorders and alignments" , with Mihyun Kang and Peter Cameron, Discrete Mathematics, 310 (2010) 591-603.

28. "Poisson approximation of the number of cliques in random intersection graphs" , with Katarzyna Rybarczyk, Journal of Applied Probability, 47 (2010) 826-840.

29. "Oil production models with normal rate curves". Probability in the Engineering and Informational Sciences, 25 (2011) 205-217.
    The normal curve has been used to fit the rate of both world and U.S.A. oil production. In this paper we give the first theoretical basis for these curve fittings. It is well known that oil field sizes can be modelled by independent samples from a lognormal distribution. We show that when field sizes are lognormally distributed, and the starting time of the production of a field is approximately a linear function of the logarithm of its size, and production of a field occurs within a small enough time interval, then the resulting total rate of production is close to being a normal curve. Here is a pdf file and a summary of the paper.

30. "The edge correlation of random forests" . Annals of Combinatorics, 15 (2011) 529-539.

31. "A Meinardus theorem with multiple singularities", with Boris Granovsky, Communications in Mathematical Physics, 314 (2012) 329-350.

32. "The asymptotic number of spanning forests of complete bipartite labelled graphs". Discrete Mathematics, 313 (2013) 1256-1261.

33. "Asymptotic enumeration of decomposable combinatorial structures with multiple singularities (Abstract), with Boris Granovsky, Electronic Notes in Discrete Mathematics 43 (2013) 15-20.

34. "Wiggles and finitely discontinuous k-to-1 functions between graphs", with John Baptist Gauci and Anthony J.W. Hilton, Journal of Graph Theory 74 (2013) 275-308.

35. "Developments in the Khintchine-Meinardus probabilistic method for asymptotic enumeration" , with Boris Granovsky, Electronic Journal of Combinatorics , 22 Paper No. 4.32 (2015), 26 pp.

36. "Bin sizes in time-inhomogeneous infinite Polya processes". Statistics and Probability Letters, 113 (2016) 49-53.

37. "Poisson approximation of counts of subgraphs in random intersection graphs" , with Katarzyna Rybarczyk, Discrete Mathematics, 340, (2017) 2183-2193.

38. "Balancing the book: is it necessary and sufficient?" , with Dominic Cortis, Journal of Gambling Business and Economics, 11, (2017) 1-6.

39. "The probability of nonexistence of a subgraph in a moderately sparse random graph " , with Nicholas Wormald, Combinatorics, Probability & Computing, 27, (2018) 672-715.

40. "The component counts of random injections " . Electronic Journal of Combinatorics , 28, Paper No. 1.5, (2021), 15 pp.

41. "The asymptotic number of weighted partitions with a given number of parts". The Ramanujan Journal, 57, (2022) 949-967. link

42. "The component counts of random functions " . Discrete Mathematics, 345, Paper No. 112977, (2022), 9 pp.

43. "An investigation into the law of small numbers using R", with Yasir Barlas (BAME Intern). Accepted for publication in Mathematics Exchange.

44. "The small cycle counts of random feedback shift registers " . The Australasian Journal of Combinatorics, 86, (2023), 414-422.

45. "Random partitions and queues " , with Alexander Gnedin. Accepted for publication in Advances in Applied Mathematics.

46. "The distribution of small subgraph counts in a moderately sparse random graph " , with Nicholas Wormald. Preprint.