Imagine $n$ $z$-vertical sticks uniformly spaced around a unit-radius circle in the $xy$-plane. At $t{=}0$, each is randomly $\epsilon$-perturbed from the vertical, and they fall under the influence of gravity. Will some sticks form a "teepee" suspended above the $xy$-plane?

Let us assume the sticks are one-dimensional segments of height $h$, perhaps $h{=}2$ so they
span the diameter,
and that their base points are pinned to the plane via universal joints.
It seems possible that a subset of sticks could fall to form a *weaving* with a cyclic
on-top-of graph, as illustrated below.

Assuming a sufficient coefficient of friction $\mu$ between pairs of sticks, it seems conceivable that such a
structure would not collapse to the plane.

What is your intuition here? For sufficiently large $n$, and adequate $h$ and $\mu$, would some sticks form a woven structure above the plane? Or would all sticks ultimately flatten to the plane? If the latter, are there natural conditions that would lead to formation of a "teepee"? I am less interested in probability calculations than in a qualitative assessment.

I've tagged this 'recreational' because it is only a peripheral spinoff of my research.

**Addendum**. It is now clear, from the comments of Scott Morrison and Rahul Narain, that
the random perturbations should be random both in direction *and magnitude*.
Otherwise, as Scott incisively observed, the sticks, with high probability, all fall without touching
one another until they reach the plane (which to me is already rather remarkable!).