List of Tables
1.1 Initialisms. 8
1.2 Discrete distributions. 9
1.3 Continuous distributions. 9
3.1 For simple symmetric random walk on {0,1,2}, this lists the possible
outcomes and their probabilities for taking two steps in the chain
given U /∈ A.47
4.1 Cases for updating the bounding chain for the swap chain for the
hard-core gas model. A ∗ indicates that there is no restriction on that
component of the vector. When N
q
= 1, let w
q
be the neighbor of v
with y(w
q
)=q.65
8.1 Comparison of RR
for Ising and RR for Ising edge provable
range of
β
where expected running time is linear in the size of the
input graph. Note here a.p.t. stands for artificial phase transition.
For instance, when
β
∈ [0,0.8779) and Δ = 3, RR for Ising is
guaranteed to run in linear time. It could still run in linear time for
larger values of
β
, but there is no a priori guarantee. 157
9.1 Comparison of h
1
(r) to (r!)
1/r
. The maximum relative error between
the two values is 6.65% at r = 3. 169
xix
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