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		   B O S T O N   U N I V E R S I T Y
                                       
		      Computer Science Department
                                       
			  C O L L O Q U I U M
                                       
		       Thursday December 22, 1994
                                       
				 3:00pm
		       (Coffee served at 2:30pm)
                                       
			 Seminar Room / MCS 135
                                       

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		  On Tails in 1-Dimensional Harnesses
				    
			      Andrei Toom
			 Incarnate Word College
				    
  As it is typical of 1-dimensional random processes with local
  interaction, components, indexed by integer numbers, interact in a local
  uniform way.  In the present case components' states are real random
  variables a_s^t, where s is in Z and t=0,1,2,3,..., and the interaction
  is linear.  A symmetric random i.i.d. `noise' \nu is added to every
  component at every time step.  Two parameters of any symmetric random
  variable \xi are used: power decay or P-decay
  
    P-decay(\xi) = \lim_{x\to\infty} (-\log_x Prob(\xi > x))

  and exponential decay or E-decay

    \hbox{E-decay}(\xi) = \lim_{x\to\infty} \log_x(-\ln Prob(\xi > x)).

  (For example, the P-decay of a Cauchy distribution equals 1 and the
  E-decay of a normal distribution equals 2.)  We prove that the limits
  (as t goes to infinity) of the differences a_s^t - a_{s-1}^t display at
  least three different modes of behavior depending on the noise:
  
  a) if P-decay(\nu) < 3/2, these differences diverge 
     and if P-decay}(\nu) > 3/2, they converge; 
  
  b) if 1 < E-decay}(\nu) \leq 3, these differences converge
     to a distribution, whose E-decay equals E-decay}(\nu);
     however, if  3 \leq E-decay(\nu), they converge 
     to a distribution, whose E-decay equals 3.

Host: Prof. Peter Gacs
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      The Spring colloquium series will begin on January 25, 1995.
For colloquium info, including directions, see http://cs-www.bu.edu/colloquium
   For more information contact Prof. Mark Crovella <crovella@bu.edu>
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