Apr 19th, 2020 - CIB Lensing: Shell by Shell Comparisons

Here, I have the change in variance, skewness, and kurtosis by [math]\displaystyle{  \ell  }[/math] ([math]\displaystyle{  \Delta \ell = 200  }[/math]) caused by weak-lensing for each CIB shell ranging from z = 0.2 to 4.2. (There are no CIB pixels at z > 4.2, and the first shell - z = 0.03 to z = 0.2 is not lensed.)

Shell 2  : 0.2 ~ 0.4    Shell 3  : 0.4 ~ 0.6    Shell 4  : 0.6 ~ 0.8    Shell 5  : 0.8 ~ 1.0    Shell 6  : 1.0 ~ 1.2   
Shell 7  : 1.2 ~ 1.4    Shell 8  : 1.4 ~ 1.6    Shell 9  : 1.6 ~ 1.8    Shell 10 : 1.8 ~ 2.0    Shell 11 : 2.0 ~ 2.2   
Shell 12 : 2.2 ~ 2.4    Shell 13 : 2.4 ~ 2.6    Shell 14 : 2.6 ~ 2.8    Shell 15 : 2.8 ~ 3.0    Shell 16 : 3.0 ~ 3.2    
Shell 17 : 3.2 ~ 3.4    Shell 18 : 3.4 ~ 3.6    Shell 19 : 3.6 ~ 3.8    Shell 20 : 3.8 ~ 4.0    Shell 21 : 4.0 ~ 4.2

- All the plots go up to [math]\displaystyle{  \ell_{max}  }[/math] (for now), and I have assumed that [math]\displaystyle{  \ell \approx 8000  }[/math] is where n-side effects kick in (dashed lines). For the 2-point and the 4-point, n-side effects seem to be less blatant, while there's a big jump for the 3-point (both field and total). 
- I will put up plots going up to [math]\displaystyle{  \ell = 8000  }[/math], once we agree that [math]\displaystyle{  \ell \gt  8000  }[/math] should be discarded. 
- As expected, the field dominates each of the shells at low [math]\displaystyle{  \ell  }[/math] for all 3 statistics, but it is hard to say where the regime change (field-dominated to halo-dominated) occurs. 
- With these plots, it is hard to tell where the scattering effects at [math]\displaystyle{  \ell \gt  2000  }[/math] evident in the lensed vs. unlensed 3-point plots are coming from. It is odd that the field [math]\displaystyle{  \kappa  }[/math], whose 3-point is orders of magnitudes lower than the total [math]\displaystyle{  \kappa  }[/math] is causing these effects.

 Shell 2  (z = 0.2 ~ 0.4) Order: [math]\displaystyle{  \lt \sigma^2\gt   }[/math], [math]\displaystyle{  \lt \sigma^3\gt   }[/math], [math]\displaystyle{  \lt \sigma^4\gt   }[/math]