<s>
The	O
contact	B-Algorithm
process	I-Algorithm
is	O
a	O
stochastic	O
process	O
used	O
to	O
model	O
population	O
growth	O
on	O
the	O
set	O
of	O
sites	O
of	O
a	O
graph	O
in	O
which	O
occupied	O
sites	O
become	O
vacant	O
at	O
a	O
constant	O
rate	O
,	O
while	O
vacant	O
sites	O
become	O
occupied	O
at	O
a	O
rate	O
proportional	O
to	O
the	O
number	O
of	O
occupied	O
neighboring	O
sites	O
.	O
</s>
<s>
The	O
contact	B-Algorithm
process	I-Algorithm
is	O
a	O
continuous-time	O
Markov	O
process	O
with	O
state	O
space	O
,	O
where	O
is	O
a	O
finite	O
or	O
countable	O
graph	O
,	O
usually	O
,	O
and	O
a	O
special	O
case	O
of	O
an	O
interacting	O
particle	O
system	O
.	O
</s>
<s>
More	O
specifically	O
,	O
the	O
dynamics	O
of	O
the	O
basic	O
contact	B-Algorithm
process	I-Algorithm
is	O
defined	O
by	O
the	O
following	O
transition	O
rates	O
:	O
at	O
site	O
,	O
</s>
<s>
The	O
contact	B-Algorithm
process	I-Algorithm
is	O
a	O
stochastic	O
process	O
that	O
is	O
closely	O
connected	O
to	O
percolation	O
theory	O
.	O
</s>
<s>
Ted	O
Harris	O
(	O
1974	O
)	O
noted	O
that	O
the	O
contact	B-Algorithm
process	I-Algorithm
on	O
when	O
infections	O
and	O
recoveries	O
can	O
occur	O
only	O
in	O
discrete	O
times	O
corresponds	O
to	O
one-step-at-a-time	O
bond	O
percolation	O
on	O
the	O
graph	O
obtained	O
by	O
orienting	O
each	O
edge	O
of	O
in	O
the	O
direction	O
of	O
increasing	O
coordinate-value	O
.	O
</s>
<s>
For	O
contact	B-Algorithm
process	I-Algorithm
on	O
all	O
integer	O
lattices	O
,	O
a	O
major	O
breakthrough	O
came	O
in	O
1990	O
when	O
Bezuidenhout	O
and	O
Grimmett	O
showed	O
that	O
the	O
contact	B-Algorithm
process	I-Algorithm
also	O
dies	O
out	O
almost	O
surely	O
at	O
the	O
critical	O
value	O
.	O
</s>
<s>
Durrett	O
conjectured	O
in	O
survey	O
papers	O
and	O
lecture	O
notes	O
during	O
the	O
80s	O
and	O
early	O
90s	O
regarding	O
the	O
central	O
limit	O
theorem	O
for	O
the	O
Harris	O
 '	O
contact	B-Algorithm
process	I-Algorithm
,	O
viz	O
.	O
</s>
