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Bjørn Kjos-Hanssen
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Why is the Gaussian so pervasive in mathematics?
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Why is the Gaussian so pervasive in mathematics?
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Why is the Gaussian so pervasive in mathematics?
@Mark: Thanks, I have added the assumption of finite variance.
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Why is the Gaussian so pervasive in mathematics?
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Why is the Gaussian so pervasive in mathematics?
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Example of a function that behaves like another function
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Example of a function that behaves like another function
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Example of a function that behaves like another function
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Path cardinality for random $(a+b)$-ary infinite trees
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Example of a function that behaves like another function
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Example of a function that behaves like another function
$f(x) = x + \frac{1}{1+|x-1|}$ satisfies (1) and what you probably mean by (2). But maybe for (3) you want something differentiable?
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Path cardinality for random $(a+b)$-ary infinite trees
@Halfdan: You're welcome. It's quite a useful result.
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Path cardinality for random $(a+b)$-ary infinite trees
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Path cardinality for random $(a+b)$-ary infinite trees
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Wiener process related counterexample
Nice. To make it even less continuous, maybe make $W(t,\omega)=w(t)+1$ whenever $w(t)$ is at a local minimum?
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 Nice Question
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Is the nearest walk to Brownian motion uniform?
@Bill Thurston: Thanks! I think this settles it. I have posted a follow-up question (how different are the two distributions as $n\rightarrow\infty$) separately: mathoverflow.net/questions/38481/…
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Is the nearest walk to Brownian motion approximately uniform?
@fedja: in that case I guess there is the Skorokhod embedding which you may be thinking of. The sequence of walks should be close to uniform and converge at a close to optimal rate for the application I have in mind (which is to answer Question 5.1 in my paper math.hawaii.edu/~bjoern/Publications/… with Szabados).
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