Measure the width of a sharp peak?

Questions
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1

Hi,
I need the width of the sharp peak that you can see in the picture below. For a given n this would be N_max - N_min as marked in the picture.
The plot is a 3D listplot over the natural numbers n and N.

I think this is important because it defines the peak like N_max >> N_max + 1 and N_min >> N_min-1. So basically I need N_max - N_min for a given n and the Programm should choose N_max and N_min automatically in a way that N_max >> N_max + 1 and N_min >> N_min - 1.

Is there some kind of build-in-function wich is able to do it or do I have to implement it myself with If-statements?

thanks in advance,

Best regards

Luca

example.jpg
example.jpg1086×556 103 KB

2

Sorry, I made a mistake there. The kriteria should be nB_an-nB_sim(N_max) >> nB_an-nB_sim(N_max + 1) and nB_an-nB_sim(N_min) >> nB_an-nB_sim(N_min - 1)

3

You did not give an example function, so I am making one up; say your “function with a peak” is:

g[x_, y_] := 1/(x^2 + 2 y^2)

and you want to know the dimensions at g=1, then this is maybe giving what you are asking for:

reg = ImplicitRegion[g[x, y] > 1, {x, y}];
CoordinateBounds[reg]
4

Thank you Henrik,
this might be helpful at a later point. But in this example there is no function. The plot is a plot of data that I got from a stochastic simulation. Sorry, I really should have been more precise.

However, I think I found a solution that works for my problem.

5

But in this example there is no function. The plot is a plot of data that I got from a stochastic simulation.

Is this really a problem? Do a ListInterpolation with your data - and you will have a function!

data2D = Table[1/(x^2 + 2 y^2), {y, -2.05, 2, .1}, {x, -2.05, 2, .1}];
(*  data2D is just an example *)
func = ListInterpolation[data2D, {{-2.05, 2}, {-2.05, 2}}];
reg = ImplicitRegion[func[x, y] > 1, {x, y}];
CoordinateBounds[reg]
6

Ok, thats a good idea. I will try it.
Thank you