R.A. Fisher, Ann. Eugenics 7, 353 1937

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R.A. Fisher, Ann. Eugenics 7, 353 1937
Kolmogoroff, I.Petrovsky, and N. Piscounoff,
Moscow Univ. Bull. Math. 1, 1-1937. P.W.
Anderson, Phys. Rev. 109, 1492 1958. M. Doi, J.
Phys. A 9, 1465 1976 H.K. Janssen, Z. Physik.
42, 141 1981. P. Grassberger, Z. Phys. B
Condens. Mat 47, 465 1982 L. Peliti, J. Phys.
France! 46, 1469 1985. M. Kardar, G. Parisi,
and Y.-C. Zhang, PRL 56,889 1986. J.L. Cardy and
U.C. Tauber, PRL 77, 4780 1996 D.C. Mattis, M.L.
Glasser, Rev. Mod. Phys. 70, 979 1998
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• Q- Discreteness / microscopic fluctuations were
  known to
• influence the approach to the equilibrium state
  (e.g. Fisher waves annihilation)
• Make perturbative corrections the value of a
  phase transition point.
• Doi, Janssen, Grassberger, Peliti, Zeldovich,
  Michailov, Cardy, Mattis and Glasser etc etc
• SO What is the novelty?
• A- Here the very character of the final state is
  totally changed (for all values)- Discreteness
  makes the difference between life and death.

N.M. Shnerb, Y. Louzoun, E. Bettelheim, and S.
Solomon, Proc. Natl. Acad. Sci. 97, 10322 2000.
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For Experts (usually they can ask, but in such a
big room I have to anticipate their thoughts)
Dont look for cheap escapes

Q- slow a(x,t) ? a0 convergence A- it is
enough a(x,t) lt m/ l to have decay at all x
Q- non-linear features in PDE
b. (a l - m ) b Db D bA- the equation is
linear in b
Q - instability of the homogenous b(x,t) b(0,t)
solution A- The solution is stable for l a 0
m lt 0