Impact
~12k
people reached
 0 posts edited
 0 helpful flags
 132 votes cast
Sep
22 
awarded  Yearling 
Jul
31 
answered  Number of samples needed as input to Bernoulli factory 
Jul
17 
answered  Reflection “monotonicity” of two point function percolation 
Apr
15 
answered  Area enclosed by Brownian motion (without winding number) 
Feb
6 
answered  Statistics of strongly connected components in random directed graphs 
Feb
6 
comment 
Statistics of strongly connected components in random directed graphs
What exactly do you mean by "nonextreme values of $p$"? For fixed $p\in(0,1)$ and $N\to\infty$ there will still be a unique component w.h.p. ... 
Dec
7 
answered  Probability that a selfavoiding walk on $\mathbb{Z}^3$ closes to a polygon 
Nov
2 
comment 
When exactly and why matrix multiplication became a part of undergraduate curriculum?
Well line 2 is the product. 
Sep
22 
awarded  Yearling 
Sep
13 
comment 
Can we give any upper bound on $E[\max_{n \leq N} X_n]$ in terms of $\max_{n \leq N} E[X_n]$
Another counterexample: take $(X_n)$ iid of mean $0$, then $\max E[X_n] = 0$. But $E[\max X_n]$ can take pretty much any value; if the support of the distribution of $X$ is not bounded above, then as $N \to \infty$ it also goes to $+\infty$. 
Sep
8 
comment 
First passage percolation on a random geometric graph in the large connectivity limit
It should not be difficult to show that $h_\infty$ does not depend on the distribution as soon as $P$ has positive density and no atom at $0$: indeed, as soon as bonds with small weight percolate "enough", they should be the only ones present on the shortest path, at least asymptotically as $\rho\to\infty$. 
Sep
8 
comment 
First passage percolation on a random geometric graph in the large connectivity limit
Do you expect the underlying point process model to be relevant? Or would you think that something similar could happen e.g. for FPP on the square lattice? 
Mar
19 
comment 
Pairs of Permutations up to Simultaneous Conjugation
(2 years later) Is there an efficient algorithmic way to check if two pairs of permutations are simultaneously conjugated like this? 
Nov
7 
comment 
Embedding points in 2D based on distance estimates?
I believe fdp and sfdp implement something like that, where by default $l_{ij}=1$ but you can specify a length for an edge to set another value.

Sep
22 
awarded  Yearling 
Sep
18 
answered  Embedding points in 2D based on distance estimates? 
Aug
16 
answered  Estimate size of graph by taking random walks 
Jun
11 
answered  Conway's game of life for random initial position 
Jun
11 
comment 
Conway's game of life for random initial position
@helper Sure, I did say "there may be", and it is quite possible that indeed density would always go to zero. I was simply pointing out that what you said could not be enough, because it did not use the specifics of GoL. And in general it is quite hard to tell what happens for a given model ... 
Jun
11 
comment 
Conway's game of life for random initial position
@helper To give a more "physical" intuition: the time needed for a box to die out will typically be exponential in the volume of the box (that's what it takes for each cell to die at the same time), while the time for a neighbouring box to make you alive again is linear in the diameter (propagation fronts move linearly). So even if one of the regions were to die out (which it will), there may be plenty of "life reservoirs" in the vicinity to resuscitate it before they themselves die. 