# What are global sensitivity and local sensitivity in differential privacy?

I am learning differential privacy now, and there is no one surrounding I can ask questions about differential privacy. I am confused about the definitions of the global sensitivity and local sensitivity.

The two definitions are from the book 《Differential Privacy and Applications》written by Tianqing Zhu, Gang Li, Wanlei Zhou, Philip S. Yu.

My understanding is:

The neighbor database only has one different record to the original database.

For the definition of global sensitivity, if $$f=\sum x_i$$, $$x_i\in \{0,1\}$$, the global sensitivity is the max value of $$\sum |f(D)-f(D')|, D'\in D^n-D$$, and there is only one different record between neighbor databases, so it equals to the max value among $$|f(D)-f(D')|$$, is obvious 1.

I am not if my understanding is right.

And how to understand local sensitivity?

Obviously, $$GS_f=max_{x}LS_f(x)$$