John Michael Hammersley. 21 March 1920 — 2 May 2004

John Hammersley was a pioneer among mathematicians, who defied classification as pure or applied; when introduced to guests at Trinity College, Oxford, he would say he did ‘difficult sums’. He believed passionately in the importance of mathematics with strong links to real–life situations and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self–avoiding walks and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem–solver, he was a leader in the movement of the 1950s and 1960s to rethink the content of school mathematics syllabuses.

[1]  J. Hammersley.  The Distribution of Distance in a Hypersphere , 1950 .

[2]  Geoffrey Grimmett,et al.  Critical probabilities for site and bond percolation models , 1998 .

[3]  William L. Roach,et al.  Optimal antithetic sampling plans , 1977 .

[4]  J. Kingman.  Subadditive Ergodic Theory , 1973 .

[5]  J. M. Hammersley,et al.  Markov fields on finite graphs and lattices , 1971 .

[6]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  Joel Friedman.  Random Polynomials and Approximate Zeros of Newton's Method , 1990, SIAM J. Comput..

[8]  H. Kesten.  The critical probability of bond percolation on the square lattice equals 1/2 , 1980 .

[9]  M. Fisher,et al.  Dimer problem in statistical mechanics-an exact result , 1961 .

[10]  G. Grimmett.  A THEOREM ABOUT RANDOM FIELDS , 1973 .

[11]  R. Kenyon.  An introduction to the dimer model , 2003, math/0310326.

[12]  J. M. Hammersley,et al.  The Zeros of a Random Polynomial , 1956 .

[13]  J. Kingman,et al.  The Ergodic Theory of Subadditive Stochastic Processes , 1968 .

[14]  B. Logan,et al.  A Variational Problem for Random Young Tableaux , 1977 .

[15]  J. M. Hammersley.  The total length of the edges of a polyhedron , 1951 .

[16]  K. Farahmand.  On the Average Number of Real Roots of a Random Algebraic Equation , 1986 .

[17]  Harry Kesten,et al.  On the Number of Self‐Avoiding Walks , 1963 .

[18]  M. Eden.  A Two-dimensional Growth Process , 1961 .

[19]  Conformally invariant scaling limits: an overview and a collection of problems , 2006, math/0602151.

[20]  E. Lieb.  A refinement of Simon's correlation inequality , 1980 .

[21]  John W. Tukey,et al.  Antithesis or regression? , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  Erhard Cramer.  Asymptotic estimators of the sample size in a record model , 2000 .

[23]  P. Erdös.  On a Conjecture of Hammersley , 1953 .

[24]  J. Hammersley.  Markovian walks on crystals , 1953 .

[25]  Shmuel Friedland,et al.  Theory of computation of multidimensional entropy with an application to the monomer-dimer problem , 2004, Adv. Appl. Math..

[27]  Alessandro Ramponi.  A note on the complex roots of complex random polynomials , 1999 .

[28]  Stauffer,et al.  Simulation of large Eden clusters. , 1986, Physical review. A, General physics.

[29]  J. Hammersley,et al.  First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory , 1965 .

[30]  Gordon Slade,et al.  Self-avoiding walk in five or more dimensions I. The critical behaviour , 1992 .

[31]  H. Poincaré,et al.  Percolation ? , 1982 .

[32]  J. Hammersley.  Percolation Processes: Lower Bounds for the Critical Probability , 1957 .

[33]  P. W. Kasteleyn.  The Statistics of Dimers on a Lattice , 1961 .

[34]  S. Smirnov.  Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits , 2001 .

[35]  Barry Simon,et al.  Correlation inequalities and the decay of correlations in ferromagnets , 1980 .

[36]  Oded Schramm,et al.  Scaling limits of loop-erased random walks and uniform spanning trees , 1999, math/9904022.

[37]  T. E. Harris.  A lower bound for the critical probability in a certain percolation process , 1960, Mathematical Proceedings of the Cambridge Philosophical Society.

[38]  J. Hammersley,et al.  A Differential Equation Connected with the Dendritic Growth of Crystals , 1989 .

[39]  M. Atiyah.  How research is carried out , 1974 .

[40]  John P. Moussouris.  Gibbs and Markov random systems with constraints , 1974 .

[41]  R. Peierls.  On Ising's model of ferromagnetism , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[42]  J. M. Hammersley,et al.  Comparison of Atom and Bond Percolation Processes , 1961 .

[43]  J. Baik,et al.  On the distribution of the length of the longest increasing subsequence of random permutations , 1998, math/9810105.

[44]  C. Domb.  On Hammersley ’ s Method for One-Dimensional Covering Problems , 2007 .