Mechanism of burning of hydrogen So I was curious regarding a simple chemical equation :

$$\ce{2 H2 + O2 -&gt; 2 H2O}$$

You add heat to the system (i.e fire) and you get water vapor.

I'm curious of understanding the mechanism, which I'm sure at this point has been well studied. 

Suppose I keep track of the location of each one of these atoms, and the energy nearby - my anticipation is that the reaction occurs when the atoms get close enough and there is sufficient energy present to conduct the reaction. Is there any way to summarize this critical point of water creation mathematically in this framework (i.e the combination of atoms being close enough and sufficient energy will make this reaction take place) - or is there a superior way?

Does anyone have any insight/publications that can help me understand the steps of water synthesis via reaction mechanism?
Martin - マーチン has given excellent answer here. I'll give here an supporting review article for your benefit, which also gives some mathematical overview: 


Louis S. Kassel, “The Mechanism of the Combustion of Hydrogen,” Chem. Rev. 1937, 21(2), 331–345 (DOI: 10.1021/cr60069a010).


Overall, mechanism can be summerized as follows:
\begin{align}
\ce{H2 + \text{heat} &amp;-&gt; 2 H^.}\\
\ce{H^. + O2 &amp;-&gt; HO-O^.}\\
\ce{HO-O^. + H2 &amp;-&gt; HO-OH + H^.}\\
\ce{H^. + HO-OH &amp;-&gt; H2O + HO^.}\\
\ce{HO^. + H2 &amp;-&gt; H2O + H^.}
\end{align}

The propagation would continue with having $\ce{H^.}$ at the end and the presence of excess $\ce{O2}$.