Probability Theory of Nonrandom Sequences

For years I tried to get people interested in the "probability theory of non-random sequences." The story behind the scary sqeuence project is rather different, yet the two are still related. For the convenience of anyone who is interested in the challenge, I've collected a few relevant references.

Two papers that made the old case most explicitly are

• Hammersley's law for the van der Corput sequence: an instance of probability theory for pseudorandom numbers,
  (with A. del Junco), Annals of Probability, 7 (1979), 267--275.
• Monotone subsequences in the sequence of fractional parts of multiples of an irrational,
  (with D. Boyd), J. Reine u. Angewante Mathematik, 306 (1979), 49--59.
• Fast sorting of Weyl sequences using comparisons,
  (with M. Ellis), SIAM Journal on Computing, 10 (1981), 88--95.
• Sizes of order statistical events of stationary processes,
  (with D. Rudolph), Annals of Probability, 8 (1980), 1079--1084.

Others with a more distant connection are

• Variations on the Monotone Subsequence Problem of Erdös and Szekeres,
  In Discrete Probability and Algorithms (Aldous, Diaconis, and Steele, eds.), 111--132, Springer Publishers, New York, 1995.
• Equidistribution in all Dimensions of Worst-case Point Sets for the Travelling Salesman Problem,
  (with T. L. Snyder), SIAM J. Discrete Mathematics, 8 (1995), 678--683.
• A priori Bounds on the Euclidean Travelling Salesman Problem,
  (with T. L. Synder), SIAM J. Computation, 24 (1995), 665--671.
• Sums of Squares of Edge Lengths and Spacefilling Curve Heuristics for the Travelling Salesman Problem,
  (with J. Gao), SIAM J. Discrete Mathematics, 7 (1994), 314--324.
• Worst-Case Greedy Matchings in the Unit Cube,
  (with T. L. Snyder) Networks, 20 (1990), 779--800.
• Kingman's subadditive ergodic theorem,
  Annales de l'Institute Henri Poincaré, 25 (1989), 93--98.
• Cost of sequential connection for points in space,
  Operations Research Letters, 8 (1989), 137--142.
• Long common subsequences and the proximity of two random strings,
  SIAM Journal on Applied Mathematics, 42 (1982), 731--737.
• Optimal sequential selection of a monotone sequence from a random sample,
  (with S. Samuels), Annals of Probability, 9 (1981), 937--947.