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0

1

$begingroup$

• Consider a random walk on an undirected graph consisting of an
  $n$-vertex path with self-loops at the both ends. With the self loops, we have $p_xy =1/2$ on all edges $left(x,yright)$, and so the stationary distribution is a uniform $1/n$ over all vertices.


• The set with minimum normalized conductance is the set $S$ with probability $pileft(Sright) leq 1/2$ having the smallest ratio of probability mass exiting it, $sum_left(x,yright) in
  left(S, overlineSright) pi_xp_xy$, to probability mass inside it, $pi(S)$.


• This set consists of the first $n/2$ vertices, for which the numerator is $1/left(2nright)$ and denominator is $1/2$. Thus, $Phileft(Sright) = 1/n$.

Can anyone explain the above paragraph more clearly ?.

convergence random-walk

share|cite|improve this question

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

asked Mar 23 at 7:17

cholechole

333

$endgroup$

add a comment | 

0

1

$begingroup$

• Consider a random walk on an undirected graph consisting of an
  $n$-vertex path with self-loops at the both ends. With the self loops, we have $p_xy =1/2$ on all edges $left(x,yright)$, and so the stationary distribution is a uniform $1/n$ over all vertices.


• The set with minimum normalized conductance is the set $S$ with probability $pileft(Sright) leq 1/2$ having the smallest ratio of probability mass exiting it, $sum_left(x,yright) in
  left(S, overlineSright) pi_xp_xy$, to probability mass inside it, $pi(S)$.


• This set consists of the first $n/2$ vertices, for which the numerator is $1/left(2nright)$ and denominator is $1/2$. Thus, $Phileft(Sright) = 1/n$.

Can anyone explain the above paragraph more clearly ?.

convergence random-walk

share|cite|improve this question

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

asked Mar 23 at 7:17

cholechole

333

$endgroup$

add a comment | 

$begingroup$

• Consider a random walk on an undirected graph consisting of an
  $n$-vertex path with self-loops at the both ends. With the self loops, we have $p_xy =1/2$ on all edges $left(x,yright)$, and so the stationary distribution is a uniform $1/n$ over all vertices.


• The set with minimum normalized conductance is the set $S$ with probability $pileft(Sright) leq 1/2$ having the smallest ratio of probability mass exiting it, $sum_left(x,yright) in
  left(S, overlineSright) pi_xp_xy$, to probability mass inside it, $pi(S)$.


• This set consists of the first $n/2$ vertices, for which the numerator is $1/left(2nright)$ and denominator is $1/2$. Thus, $Phileft(Sright) = 1/n$.

Can anyone explain the above paragraph more clearly ?.

convergence random-walk

share|cite|improve this question

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

asked Mar 23 at 7:17

cholechole

333

$endgroup$

share|cite|improve this question

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

asked Mar 23 at 7:17

cholechole

333

share|cite|improve this question

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

asked Mar 23 at 7:17

cholechole

333

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

edited Mar 30 at 4:57

Felix Marin

68.9k7110147

asked Mar 23 at 7:17

cholechole

333

asked Mar 23 at 7:17

cholechole

333