shader for 2D mesh with noise transparency at the edge

i am looking for way how to create effect similar to inner glow or inner shadow

i have procedurally generated 2D mesh, i need to use two textures on it 1st is the diffuse texture and the 2nd is soft gradient at the edge of the outer shape of the mesh, i can do it with 2 groups of vertices of course, but i also need to have some random noise in the edge alpha fade, so i thought i might use grayscale texture and somehow map it around the edge

however i don't know how do i recognize if the vertex is at the edge or not and i don't know how to map texture around the edge

thanks in advance for any idea