How to model randomness in validators selection in PoS? I searched a lot here and on the Internet to figure how how randomness selection of validators in PoS works? I understand it is a random selection based on fraction of stake a validator has, similar to PoW.

In PoW, we can model block arrival as a possion process. E.g., if block interval is 10 seconds,, we expect on average a block to be created each 10 seconds. You can get two blocks where the time between them less than a second (hence memoryless process). The chance each miner has for each block depends on its hash power fraction, but random in terms of assigning miners to blocks.

Now, how block arrival and assignment differs in PoS? from what i think is the same as in PoW. From other sources, i read time is divided into slots, where each slot is assigned to a validator (say deterministic). But not really understand how this differs from PoW. Any plain English explannation is appreciated (without too much technical details).
I understand it is a random selection based on fraction of stake a validator has, similar to PoW.


Not correct. In PoW, any miner can mine the next block. In PoS, a specific validator is chosen by the protocol that has the right to form/propose the next block.


  The chance each miner has for each block depends on its hash power fraction, but random in terms of assigning miners to blocks.


The first part is correct that the chance a miner has depends on the hash power fraction. However, no miner is 'assigned.' Any miner can form the next block in the blockchain provided the block is valid and its header hash meets the target requirements.


  How block arrival and assignment differs in PoS?


There is no one protocol set in stone that determines how the next block validator is chosen. (1) Peercoin (the first coin to implement PoS consensus along with PoW) used coin age (no. of coins x no of days the coins are in the wallet) to determine the next validator. (2) Then there is a hash selector (Ouroboros Praos protocol) wherein you take the current date and time, sign it with your private key and then check if it is less than the difficulty target. If yes, you are selected as the next validator. (3) There was one method where the randomness of the next block will depend on the signature of the current block (this method is now defunct due to potential vulnerabilities.)