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東京確率論セミナー
過去の記録 ～10/31｜次回の予定｜今後の予定 11/01～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 佐々田槙子、中島秀太（明治大学）、星野壮登（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
次回の予定
2025年11月06日(木)
14:00-17:30 数理科学研究科棟(駒場) 128号室
講演は木曜日で開始時間が早まっています。教室は１２８です。今日はTea Time はありません。
Mo Dick Wong 氏 (Durham University) 14:00-15:30
On the limiting distribution of partial sums of random multiplicative functions
de Finetti Random Walks on a Hypercube and Gaussian Fields
講演は木曜日で開始時間が早まっています。教室は１２８です。今日はTea Time はありません。
Mo Dick Wong 氏 (Durham University) 14:00-15:30
On the limiting distribution of partial sums of random multiplicative functions
[ 講演概要 ]
Consider a random walk associated with a Steinhaus multiplicative function (i.e. the increments are completely multiplicative and uniformly distributed on the complex unit circle): what can we say about its asymptotic behaviour? In his seminal work, Harper resolved a conjecture of Helson by showing that low fractional moments exhibit better-than-square-root cancellation, but the asymptotic distribution remained a mystery and was left as an open problem. In this talk, I will first explain some history and the number-theoretic motivations behind this model, and then present a central limit theorem that features a nonstandard renormalisation as well as a random variance described by the Riemann Zeta function on the critical line. I will highlight the probabilistic aspects of our proof, and in particular discuss a universality result for critical non-Gaussian multiplicative chaos. This is based on joint work with Ofir Gorodetsky.
Robert Griffiths 氏 (Monash University) 16:00-17:30Consider a random walk associated with a Steinhaus multiplicative function (i.e. the increments are completely multiplicative and uniformly distributed on the complex unit circle): what can we say about its asymptotic behaviour? In his seminal work, Harper resolved a conjecture of Helson by showing that low fractional moments exhibit better-than-square-root cancellation, but the asymptotic distribution remained a mystery and was left as an open problem. In this talk, I will first explain some history and the number-theoretic motivations behind this model, and then present a central limit theorem that features a nonstandard renormalisation as well as a random variance described by the Riemann Zeta function on the critical line. I will highlight the probabilistic aspects of our proof, and in particular discuss a universality result for critical non-Gaussian multiplicative chaos. This is based on joint work with Ofir Gorodetsky.
de Finetti Random Walks on a Hypercube and Gaussian Fields
[ 講演概要 ]
This talk will discuss a random walk on the infinite hypercube,
Xt+1 = Xt + Zt mod 2.
The increments (Zt) are i.i.d. with entries that form an infinite exchange- able {0,1} sequence, a de Finetti sequence. There is geometric killing in the random walk. A Gaussian free field (gx)x∈{0,1}∞ is associated with the random walk by taking the covariance function to be proportional to the Green function of the random walk. The Green function and a strong rep- resentation for (gx) are characterized by a negative binomial point process which involves the de Finetti measure of the increments of the random walk.
This talk will discuss a random walk on the infinite hypercube,
Xt+1 = Xt + Zt mod 2.
The increments (Zt) are i.i.d. with entries that form an infinite exchange- able {0,1} sequence, a de Finetti sequence. There is geometric killing in the random walk. A Gaussian free field (gx)x∈{0,1}∞ is associated with the random walk by taking the covariance function to be proportional to the Green function of the random walk. The Green function and a strong rep- resentation for (gx) are characterized by a negative binomial point process which involves the de Finetti measure of the increments of the random walk.
