All Questions

I am in the process of writing some self-contained notes on probability theory in spaces of distributions, for the purposes of statistical mechanics and quantum field theory. Perhaps the simplest ...

Consider the function $$f_{n}(x)=e^{-x^2}x^n.$$ and the function $$h_p(x):=e^{-\vert x \vert^p}.$$ My goal is to analyze $$ F_p(y):=\frac{(f_2*h_p)(y)}{(f_0*h_p)(y)}- \left(\frac{(f_1*h_p)(y) }{(f_0*...

Consider the lattice $\mathbb Z^2$ and take iid random variables $Y_e$ on all edges $e$ of the graph. We then define random variables $X_i:=\sum_{e \text{ adjacent to } i}Y_e.$ In other words: For ...