Doing some quick math, the shell in which they'll be orbiting has a surface area of 373,367,808km. With ~7000 satellites, an even distribution would leave them 533,382 km between satellites. All the satellites have station keeping thrusters to keep them in LEO with drag. Keeping them from running into each other is probably pretty simple, in comparison to the other challenges they'll need to solve.
Doing some quick math, the shell in which they'll be orbiting has a surface area of 373,367,808km. With ~7000 satellites, an even distribution would leave them 533,382 km between satellites. All the satellites have station keeping thrusters to keep them in LEO with drag. Keeping them from running into each other is probably pretty simple, in comparison to the other challenges they'll need to solve.