Publications and Preprints of Dudley Stark

"First occurence in pairs of long words: a Penneyante
conjecture of Pevzner"
,
Combinatorics, Probability & Computing, 4 (1995), 279285.

"Total variation asymptotics for Poisson process
approximations of logarithmic combinatorial assemblies"
,
with Richard Arratia and Simon Tavaré,
Annals of Probability, 23 (1995), 13471388

"A Darboux type theorem for slowly varying functions"
,
with Boele Braaksma,
Journal of Combinatorial Theory, Series A, 77 (1997), 5166.

"Explicit nonzero limits of total variation distance
in independent Poisson approximations of logarithmic
combinatorial assemblies"
,
Combinatorics, Probability & Computing, 6 (1997), 87106.

"Total variation asymptotics for independent process
approximations of logarithmic multisets and selections"
,
Random Structures & Algorithms, 11 (1997), 5180.

"Asymptotic enumeration
of convex polygons"
,
with Nicholas Wormald,
Journal of Combinatorial Theory, Series A, 80 (1997), 196217.

"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.

"Total variation asymptotics for refined Poisson process approximations of logarithmic combinatorial
assemblies"
,
Combinatorics, Probability & Computing, 8 (1999), 567598.

"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), 613626.

"The characteristic polynomial of a random permutation matrix"
,
with
Ben Hambly, Peter Keevash and Neil O'Connell,
Stochastic Processes and Applications, 90 (2000), 335346.

"Compound Poisson approximations of subgraph counts in random graphs"
,
Random Structures & Algorithms, 18 (2001), 3960.

"Information loss in riffle shuffling"
,
with Ayalvadi Ganesh and Neil O'Connell,
Combinatorics, Probability & Computing, 11 (2002), 7995.

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

"Information loss in top to random shuffling"
,
Combinatorics, Probability & Computing, 11 (2002), 607627.

"The vertex degree distribution of random intersection graphs"
.
Random Structures & Algorithms, 24 (2004), 249258.

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

"Asymptotic enumeration and logical limit laws for expansive multisets"
,
with
Boris Granovsky,
Journal of the London Mathematical Society (2), 73 (2006),
252272.

"Logical limit laws for logarthmic structures"
.
Mathematical Proceedings of the Cambridge Philosophical
Society, 140 (2006), 537544.

"Asymptotic enumeration of incidence matrices"
,
with
Peter Cameron and Thomas Prellberg,
Journal of Physics: Conference Series , 42 (2006), 5970.

"The degree of a typical vertex in generalized random intersection graph
models"
,
with
Jerzy Jaworski and Michal Karonski,
Discrete Mathematics, 306 (2006), 21522165.

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

"The vertex degree distribution of passive random intersection graph
models"
,
with
Jerzy Jaworski,
Combinatorics, Probability & Computing, 17 (2008), 549558.

"Meinardus' theorem on weighted partitions: extensions and
a probabilistic proof"
,
with Boris Ganovsky and Michael Erlihson,
Advances in Applied Mathematics, 41 (2008), 307328.

"Peak production in an oil depletion model with triangular field profiles"
.
Journal of Interdisciplinary Mathematics,
11 (2008), 695706.
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 Hubberttype curves. Here is a
pdf file of the paper.
I've written a
summary of this paper for
The Oil Drum

"The limit of the statistic R/P in models of oil discovery and
production"
.
Applied Mathematical Sciences, 3 (2009), 27032706.
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

"Asymptotic enumeration of 2covers and line graphs"
,
with Peter Cameron and Thomas Prellberg,
Discrete Mathematics, 310 (2010) 230240.

"Random preorders and alignments"
, with Mihyun Kang and Peter Cameron,
Discrete Mathematics, 310 (2010) 591603.

"Poisson approximation of the number of cliques in random intersection
graphs"
,
with
Katarzyna Rybarczyk,
Journal of Applied Probability, 47 (2010) 826840.

"Oil production models with normal rate curves".
Probability in the Engineering and Informational Sciences,
25 (2011) 205217.
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.

"The edge correlation of random forests"
.
Annals of Combinatorics, 15 (2011) 529539.

"A Meinardus theorem with multiple singularities",
with Boris Granovsky,
Communications in Mathematical Physics, 314 (2012) 329350.

"The asymptotic number of spanning forests of complete bipartite labelled graphs".
Discrete Mathematics, 313 (2013) 12561261.

"Asymptotic enumeration of decomposable combinatorial structures with
multiple singularities (Abstract), with Boris Granovsky,
Electronic Notes in Discrete Mathematics
43 (2013) 1520.

"Wiggles and finitely discontinuous kto1
functions between graphs", with
John Baptist Gauci and Anthony J.W. Hilton,
Journal of Graph Theory
74 (2013) 275308.

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

"Bin sizes in timeinhomogeneous infinite Polya processes".
Statistics and Probability Letters, 113 (2016) 4953.

"Poisson approximation of counts of subgraphs
in random intersection graphs"
,
with
Katarzyna Rybarczyk,
Discrete Mathematics, 340, (2017) 21832193.

"Balancing the book: is it necessary and sufficient?" ,
with
Dominic Cortis,
Journal of Gambling Business and Economics,
11, (2017) 16.

"The probability of nonexistence of a subgraph in a moderately sparse
random graph " ,
with
Nicholas Wormald,
Combinatorics, Probability & Computing,
27, (2018) 672715.

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

"The asymptotic
number of weighted partitions with a given number of parts".
The Ramanujan Journal, 57, (2022) 949967.
link

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

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

"The small cycle counts of random feedback shift registers
" .
The Australasian Journal of Combinatorics, 86, (2023), 414422.

"Random partitions and queues
" ,
with Alexander Gnedin. Advances in Applied Mathematics, 149 (2023) 102549.

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

"Singlecell mutational burden distributions in birthdeath processes
" ,
with
Christo Morison and Weini Huang. Submitted.
Book Reviews

"Logarithmic Combinatorial Structures:
A Probabilistic Approach by Richard Arratia, A. D. Barbour,
and Simon Tavare". London Mathematical Society Bulletin,
(2005), 157159.
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