Cauchy-Lorentz distribution limit

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The discussion centers on whether the limit of the Lorentz distribution as gamma approaches zero converges to the Dirac delta function. It is suggested that the Dirac delta function can be viewed as the limit of the Cauchy-Lorentz distribution, emphasizing its probabilistic nature with an area of one. The conversation highlights that while the Dirac delta is often derived from the Gaussian distribution, this is not the only approach. Participants are encouraged to share their agreement or disagreement with this perspective. The exploration of this limit raises interesting questions about the relationship between these mathematical functions.
TheDestroyer
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The Lorentz distribution is in this link

http://en.wikipedia.org/wiki/Cauchy_distribution

My question is the following, does the limit gamma -> zero, convert this function to Dirac delta?

Thank you
 
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Yes, I think. The dirac delta function is usually explained using a limit of the Gaussian distribution, however that is not necessary.

The DDF can be thought of the limit of the Cauchy-Lorentz distribution since it is probabilistic( which means the area is 1)and the limiting process will make it shoot upwards like the DDF.
 
Thank you. If you guys agree, or disagree, say :)
 

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