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Consider a scenario where a security can be exchanged on two exchanges A and B. A trader who has access to A and B with same execution probabilities submit an order and split it between A and B according to the liquidity availible, thus, minimizing the total price impact. In a perfect world, does it lead to an elimination of post-order roundtrip arbitrage between A and B ? What if the price between A and B differ ?

Thanks :)

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