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Aug
29
comment Random walks on connected finite graphs
There is a path of length at most $n-1$.
Aug
29
comment Random walks on connected finite graphs
I was curious if there is a way to argue this using the idea of the Markov matrix $M$ where $M_{ij}$ is the probability of transition of the walker from vertex $j$ to $i$ i.e $1/deg(j)$. Then given an initial vertex $a$ and a final vertex $b$ and $n$, we have that $(M^n)_{ab}$ is the probability for the walker to go from $b$ to $a$ in $n$ steps. Now can one show that for $n\rightarrow \infty$ this matrix element tends to $1$?
Aug
29
comment Random walks on connected finite graphs
Can you kindly explain this idea of "diameter"?
Aug
29
comment Random walks on connected finite graphs
@user133281 Yes - that can be one meaning. Or one can also say that if one is given two specific vertices say $a$ and $b$ then with probability $1$ the random walker will reach $b$ from $a$ if allowed infinite steps.
Aug
29
asked Random walks on connected finite graphs
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
And to make "k" the minimum filled label, why do you need exactly the first (k-1) boxes to be empty? One could have a situation where all the balls are in the k^th box and then the minimum label is still "k".
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
When you write that expression, $^nC_1 \frac{(n-1)^{(n-1)} }{n^n}$ aren't you allowing for there to be multiple boxes with a single ball? Then the events you have summed over in calculating $E(M)$ are not disjoint - right?
Aug
22
revised About putting $n$ distinct balls into $n$ distinct boxes.
added 44 characters in body
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
@DPoole The minimum value of the label among the boxes which are non-empty.
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
@deinst Can you kindly write in details? If you could state the exact answers you have then I can match them for a start.
Aug
22
asked About putting $n$ distinct balls into $n$ distinct boxes.
Jul
2
awarded  Curious
Jun
25
revised How to power series expand determinants?
edited body
Jun
25
comment How to power series expand determinants?
@Muphrid Yes. This is what one needs to do for any Graham-Fefferman expansion. I am trying to understand how one does that!
Jun
24
revised How to power series expand determinants?
added 301 characters in body
Jun
24
revised How to power series expand determinants?
added 8 characters in body
Jun
24
asked How to power series expand determinants?
Jun
9
revised Using the Hodge theorem to decompose the metric tensor
added 71 characters in body
Jun
9
asked Using the Hodge theorem to decompose the metric tensor
May
10
comment Taking limits on integration limits.
@SiddharthVenkatesh Thanks! And would anything in the prescription change if the lower limit were not $0$ but some another function say $f_2(\epsilon)$?