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Results tagged with pr.probability
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user 9232
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Poisson spacings?
Assume that for every $n\geq 1 $ we are given a real random variable $X_n$ such that $(X_n-n)/\sqrt n$ follows the standard normal distribution. Furthermore, assume that the $X_n$ are independent. Fix …
- 3,062
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How many moments determine a normal distribution?
I know that a Gaussian distribuion is determined by its moments. I was wondering if there is a result of the form:
if we know that the first thousand moments of a random variable are Gaussian, then is …
- 3,062
2
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Least positive value of a random polynomial
Fix a positive even integer $d$ and consider the polynomial $f(x)=c_d x^d+\ldots+c_1x+c_0$, where the $c_i$ are independent random variables that follow the uniform distribution in the interval $[-1,1 …
- 3,062
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On the number of consecutive divisors of an integer
Define for $n \in \mathbb{N}$ the function $$\tau_1(n):=\sum_{\substack{d|n, \\ d+1|n}}1,$$ i.e. the number of consecutive divisors of an integer. The average of $\tau_1(n)$ is $1$ since $$\sum_{n\leq …
- 3,062