I am quite new to random walk theory so please excuse my rather simply put question but I am wondering how can quant trading desks and other algorithmic trading firms exist if there is the random walk theory? Wouldn't it suggest if there is the random walk theory, noone can not outperform the market?
And as a second part of the question regarding random walks: Is there any research on random walks and the behaviour of limit order books? i.e. this Paper by Rosu models a limit-order book using Markov processes and a Markov perfect equilibirium: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=710841
Would a random walk in order book dynamics not suggest that models like this aren't of any use? To my understanding such a model makes sense, as there are agents interacting in a limit order-book that are to a substantial part algo trading driven and therefore they follow some kind of pattern that (should) make it possible to model this behaviour of such an limit order-book?