The book that young Olivia is reading in "Subject 13" is called Winter's Tale by Mark Helprin.

Wikipedia has some interesting things to say about the book:

The title Winter's Tale is a reference to the similarly named Shakespeare play. In that play, as in this book, a major character disappears for years, only to return after a long and unexplained absence, unharmed, transformed, and redeemed.[Peter?]
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Winter's Tale is a 1983 novel by Mark Helprin. It takes place in a mythic New York City, markedly different than our own.[Alternate Universe?]
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New York City is subsumed in arctic winds, dark nights, and white lights, its life unfolds, for it is an extraordinary hive of the imagination, the greatest house ever built, and nothing exists that can check its vitality.[Is this why it snowed in the tulip field?]

The most interesting part of the book is name of the main character Peter Lake!

FYI, the paperback edition has a different cover, but if you want the exact same book Olivia is reading, hardcover versions with the same cover are available in the Amazon used books section.