We measure the price impacts across a correlated financial market by the responses to single and multiple trades. Focusing on the primary responses, we use an event time scale. We quantify the asymmetries of the distributions and of the market structures of cross-impacts, and find that the impacts across the market are asymmetric and non-random. Using spectral statistics and Shannon entropy, we visualize the asymmetric information in market impacts. Also, we introduce an entropy of impacts to estimate the randomness between stocks. We show that the useful information is encoded in the impacts corresponding to the small entropy. The stocks with large number of trades are more likely to impact others, while the less traded stocks have higher probability to be impacted by others.
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