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  • W. Allee. Animal aggregations : A study in general sociology. University of Chicago Press, Chicago, USA, 1931.
  • S. J. Altschuler, S. B. Angenent, Y. Wang, and L. F. Wu. On the spontaneous emergence of cell polarity. Nature, 454:886--889, 2008.
  • Ball, Karen; Kurtz, Thomas G.; Popovic, Lea; Rempala, Greg. Asymptotic analysis of multiscale approximations to reaction networks. Ann. Appl. Probab. 16 (2006), no. 4, 1925--1961. MR2288709
  • A. Butty, N. Perrinjaquet, A. Petit, M. Jaquenoud, J. Segall, K. Hofmann, C. Zwahlen, and M. Peter. A positive feedback loop stabilizes the guanine-nucleotide exchange factor cdc24 at sites of polarization. EMBO Journal, 21:1565--1576, 2002.
  • Y. Cao, D. T. Gillespie, and L. R. Petzold. The slow-scale stochastic simulation algorithm. The Journal of Chemical Physics, 122(1), Jan. 2005.
  • Chicone, Carmen. Ordinary differential equations with applications. Texts in Applied Mathematics, 34. Springer-Verlag, New York, 1999. xvi+561 pp. ISBN: 0-387-98535-2 MR1707333
  • Dawson, D. A.; Maisonneuve, B.; Spencer, J. École d'Été de Probabilités de Saint-Flour XXI—1991. [Saint-Flour Summer School on Probability Theory XXI—1991] Papers from the school held in Saint-Flour, August 18–September 4, 1991. Edited by P. L. Hennequin. Lecture Notes in Mathematics, 1541. Springer-Verlag, Berlin, 1993. viii+352 pp. ISBN: 3-540-56622-8 MR1242574
  • Donnelly, Peter; Kurtz, Thomas G. Genealogical processes for Fleming-Viot models with selection and recombination. Ann. Appl. Probab. 9 (1999), no. 4, 1091--1148. MR1728556
  • Donnelly, Peter; Kurtz, Thomas G. Particle representations for measure-valued population models. Ann. Probab. 27 (1999), no. 1, 166--205. MR1681126
  • D. G. Drubin and W. J. Nelson. Origins of cell polarity. Cell, 84:335--344, 1996.
  • Ethier, S. N.; Kurtz, Thomas G. The infinitely-many-neutral-alleles diffusion model. Adv. in Appl. Probab. 13 (1981), no. 3, 429--452. MR0615945
  • Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085
  • Ethier, S. N.; Kurtz, Thomas G. Fleming-Viot processes in population genetics. SIAM J. Control Optim. 31 (1993), no. 2, 345--386. MR1205982
  • Ewens, Warren J. Mathematical population genetics. I. Theoretical introduction. Second edition. Interdisciplinary Applied Mathematics, 27. Springer-Verlag, New York, 2004. xx+417 pp. ISBN: 0-387-20191-2 MR2026891
  • Feng, Shui. The Poisson-Dirichlet distribution and related topics. Models and asymptotic behaviors. Probability and its Applications (New York). Springer, Heidelberg, 2010. xiv+218 pp. ISBN: 978-3-642-11193-8 MR2663265
  • Fife, Paul C. Mathematical aspects of reacting and diffusing systems. Lecture Notes in Biomathematics, 28. Springer-Verlag, Berlin-New York, 1979. iv+185 pp. ISBN: 3-540-09117-3 MR0527914
  • Fleming, Wendell H.; Viot, Michel. Some measure-valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28 (1979), no. 5, 817--843. MR0542340
  • A. Gierer and H. Meinhardt. A theory of biological pattern formation. Kybernetik, 12:30--39, 1972.
  • Gupta, Ankit. Stochastic model for cell polarity. Ann. Appl. Probab. 22 (2012), no. 2, 827--859. MR2953570
  • J. E. Irazoqui, A. S. Gladfelter, and D. J. Lew. Scaffold-mediated symmetry breaking by cdc42p. Nature Cell Biology, 5:1062--1070, 2003.
  • Joffe, A.; Métivier, M. Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. in Appl. Probab. 18 (1986), no. 1, 20--65. MR0827331
  • H.-W. Kang and T. G. Kurtz. Separation of time-scales and model reduction for stochastic reaction networks. The Annals of Applied Probability (to appear), 2012.
  • Katzenberger, G. S. Solutions of a stochastic differential equation forced onto a manifold by a large drift. Ann. Probab. 19 (1991), no. 4, 1587--1628. MR1127717
  • Khalil, Hassan K. Nonlinear systems. Macmillan Publishing Company, New York, 1992. xii+564 pp. ISBN: 0-02-363541-X MR1201326
  • M. Kimura. Solution of a process of random genetic drift with a continuous model. Proceedings of the National Academy of Sciences, 41(3):144--150, 1955.
  • M. Kimura and J. Crow. The number of alleles that can be maintained in a finite population. Genetics, 49:725--738, 1964.
  • Kingman, J. F. C.; Taylor, S. J.; Hawkes, A. G.; Walker, A. M.; Cox, David Roxbee; Smith, A. F. M.; Hill, B. M.; Burville, P. J.; Leonard, T. Random discrete distribution. With a discussion by S. J. Taylor, A. G. Hawkes, A. M. Walker, D. R. Cox, A. F. M. Smith, B. M. Hill, P. J. Burville, T. Leonard and a reply by the author. J. Roy. Statist. Soc. Ser. B 37 (1975), 1--22. MR0368264
  • A. Lotka. Elements of Physical Biology. The Williams and Watkins company, Baltimore, 1925.
  • Moran, P. A. P. Random processes in genetics. Proc. Cambridge Philos. Soc. 54 1958 60--71. MR0127989
  • R. M. Nisbet and W. S. C. Gurney. Modeling fluctuating populations. Wiley, 1982.
  • Oelschläger, Karl. On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes. Probab. Theory Related Fields 82 (1989), no. 4, 565--586. MR1002901
  • Seneta, E. Non-negative matrices and Markov chains. Revised reprint of the second (1981) edition [Springer-Verlag, New York; MR0719544]. Springer Series in Statistics. Springer, New York, 2006. xvi+287 pp. ISBN: 978-0387-29765-1; 0-387-29765-0 MR2209438
  • M. Sohrmann and M. Peter. Polarizing without a c(l)ue. Trends Cell Biology, 13:526--533, 2003.
  • T. Takaku, K. Ogura, H. Kumeta, N. Yoshida, and F. Inagaki. Solution structure of a novel cdc42 binding module of bem1 and its interaction with ste20 and cdc42. Journal of Biological Chemistry, 285(25):19346--19353, 2010.
  • Thieme, Horst R. Mathematics in population biology. Princeton Series in Theoretical and Computational Biology. Princeton University Press, Princeton, NJ, 2003. xx+543 pp. ISBN: 0-691-09290-7; 0-691-09291-5 MR1993355
  • Varah, J. M. A lower bound for the smallest singular value of a matrix. Linear Algebra and Appl. 11 (1975), 3--5. MR0371929
  • P. Verhulst. Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et Physique, 10:113--121, 1838.
  • V. Volterra. Fluctuations in the abundance of a species considered mathematically. Nature, 118:558--560, 1926.
  • O. Weiner, P. Neilsen, G. Prestwich, M. Kirschner, L. Cantley, and H. Bourne. A ptdinsp(3)- and rho gtpase-mediated positive feedback loop regulates neutrophil polarity. Nature Cell Biology, 4(5):509--13, 2002.
  • S. Wright. Evolution in Mendelian populations. Genetics, 16(2):97--159, 1931.

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