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Stochastics 

Emily Yin

random walk
1. a succession of steps following no discernible pattern

Flip a coin. If heads, take one step forward. If tails, move one step back. Mathematicians call this kind of motion a random walk.

Fact: random walks have been used to simulate events as varied as a foraging animal’s search path, a drunkard’s walk, and a molecule’s trajectory through space.

As an undergrad in college, learning statistics for the first time, Lucy finds it all very poetic. What are models but biographies, the story of a life?



lifetime
1. a random variable specified by the deterioration function of the subject in question.

Three weeks ago, Lucy’s uncle had phoned from Beijing. I think it’s time. He’d warned her, always in conditionals, of the day her grandfather would have to be shunted into a nursing home. If he forgets X within a span of Y weeks. If his dementia progresses beyond a certain point. Lucy never questioned her uncle too carefully during these weekly reports, afraid of what she’d learn. But then came the latest call, and her stubborn ignorance could no longer hold.

You’re coming back? For how long? he’d asked. She had no answer, but it didn’t matter much. Lucy had no real attachment to the New England suburb in which she’d been born and raised, little love for the two-story colonials and sickly-green lawns that populated its streets. One of those ‘excellent sheep’ the op-eds scorned, she’d dutifully secured admission to college—one prestigious enough to warrant false modesty—eked out degrees in statistics and literature, and, having satisfied parental expectations, found herself at a dead end.

Since childhood, while others played make-believe with Barbies and trucks, Lucy had written imaginary worlds into existence. Where it really mattered, though, imagination failed; she just couldn’t seem to script out the course of her life. There were vague plans of applying to law school, if only to defer the responsibilities of the real world, but LSAT prep gave way to one gap year and then another. And so it was not very difficult to uproot. It was not difficult at all.



memoryless
1. a process that is independent of its history

Her grandparents’ apartment building, where she’s to take up residence during her stay in Beijing, is a tessellation of worn tiles, windows, and balconies repeated ad infinitum. It’s rather hideous from an aesthetic standpoint; even so, she aches for it. The beauty of the scene, Lucy thinks, lies in its agelessness; in a world where everything breaks down and nothing stays the same, this building remains entirely faithful to her memory. From each balcony: underwear flapping in the breeze. The light in constant motion, flickering breathlessly across the pavement and the trees. Even the two mom-and-pop breakfast places, infamous for their tepid service and greasy fare, are somehow still in business.



regression analysis
1. a set of statistical procedures for estimating relationships

Lucy traverses the apartment as she would a museum or memorial, start-stop start-stop, movement punctuated by reverential pauses. Exhibit A: an oil painting riddled with holes. We got your father a toy bow for Christmas, which he promptly put to good use. Exhibit B: a photographic montage. Lucy in second grade, gap-toothed and stupidly happy; Lucy in third, fourth, fifth grade, looking lovelier—and unhappier—with each passing year. Some people carve grooves in their skin or chase after chemical highs; for her the injury has always been stealthier, corrosive thoughts sandpapering the mind, you useless, useless, useless girl. Exhibit C: the washing machine. She steps onto the balcony, placing a palm on the cool white surface. The cat used to perch there. She’d loved it fiercely but never mourned its death. Now, in the shadowed apartment, tears mist over her eyes.

The last time Lucy visited had been her junior year of high school. She and her grandparents spent much of the three weeks circling each other politely, wordlessly. Years of disuse had whittled her mother tongue down to a repertoire of please, thank you, how are you doing. Frustrated by the futility of it all, she began to speak less and less, trading monosyllabic responses for nods.

On the last day, though, Lucy rose from her stupor and walked around the apartment. Here was the plaster mold of her hand, there the fine china her grandmother never used. The farewell tour ended on the balcony. Someone carefully slid open the glass door and crossed the threshold—her grandfather. Only he’d be up so early. Lucy waited for him to say something. Anything. Just one word, she thought, and the vast gulf between them would collapse.

Nǐ zhīdào ma, he said, gripping her wrist almost violently. Yéye zuì shěbude nǐ. You know, it’s always hardest for me to part with you. Lucy wanted to apologize for sending so many of his phone calls to voicemail, for her foolish pride, for her unwillingness, even then, to convey her feelings in a language he’d understand. But she couldn’t say a word.



risk aversion
1. a tendency to avoid risk in the face of uncertainty

The assisted living residence is a gray industrial building on the outskirts of Beijing. After checking in, Lucy takes the elevator to the seventh floor, raps on his door. Someone shuffles across the room. The delay is nearly unbearable. Then the door opens and she’s face-to-face with her grandfather, his too-bright eyes and mottled skin, an oversized FIFA baseball cap. He studies her as if she’s not a person, a real flesh-and-blood human being, but a curious sight, and she returns his gaze. The longer she stares, the more unfamiliar he seems—who is this stranger standing before her?

The man’s thin mouth contorts into a smile, a smile Lucy reflexively mirrors. And then: “Who are you?” Lucy’s lips, still lifted up in that grotesque parody of joy, start to quiver from the strain. She wishes she could cover her ears. She wishes she could screw her eyes shut like a child, make it all go away—or, better yet, grab him by the shoulders, wake up it’s me, shake him back to life—instead, she leaves.



expectation
1. the long-run average value of repeated experiments

It’s the uncertainty that makes it so difficult. Sometimes he recognizes her; sometimes he doesn’t. Quick: compute the probability of each event, specify the distribution. In his moments of lucidity, he tells Lucy to go back and live her life. It doesn’t matter where you’re going, he says, as long as you’re going somewhere. Second year of college, sitting in a probability class: a pathological distribution is one whose properties are considered atypically bad or counterintuitive. Lucy had thought there was something delightfully charming about it at the time. Count on a hopeless romantic to find beauty where there’s none. It took more than a diploma for her to learn that logic is indifferent. The numbers don’t always make sense; sometimes they’re unforgivably ugly.

Less than two months in, she decides to return to the United States. During her last visit, Lucy’s grandfather greets her affably at the door, the way he would any stranger passing by. She gropes for the right words, maudlin but true, I love you, I’m sorry, I never really tried, things she ought to have said years ago. But such histrionics would only upset him; silence is her price to pay.

Through the bay window, Beijing splays out before Lucy’s eyes—dearest Beijing, her most bitter love, skyscrapers eliding into pale white sky, convenience stores, her grandfather reaching for pocket change, here, pick out anything you want, hutongs, her grandfather bartering for a backpack with dancing ballerinas, stern man softened, inexplicably, by a foolish little girl, three thousand sunsets come and gone, same girl, now long-limbed and wary-eyed, pointing to a coat on a department store shelf, can I try this on, foreign-sounding words spilling from native mouth, shopkeeper’s eyes flickering, where are you from, junior year of high school, July 29th, 5:35 a.m., it’s always hardest for me to part with you, the admission she cannot make, I know, grandfather, I know—maybe Lucy was wrong to think dementia a curse. After all, remembering is its own kind of torment.