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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 215
/
2
/
b
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 215
2
b
2026-09-28
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The worst-case
distance
to stationarity is
d
(
t
)
=
max
σ
∥
P
t
(
σ
,
⋅
)
−
π
β
∥
TV
.
(1)
The
Path coupling theorem
says that if
a
coupling
contracts an
integer
-valued
path metric
by
a
factor
α
<
1
for every adjacent
pair
, then
d
(
t
)
≤
diam
(
Ω
)
α
t
.
(2)
Ancestors
(11)
b
2
Paper 215
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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