- 2025/11/25(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Zhao Mingdong(大阪大学)
The asymptotic behavior of the renormalized zero resolvent of Lévy
processes under regular variation conditions
As an analogue to the explicit formula in the stable case, the
asymptotic behavior at the origin of the renormalized zero resolvent of
one-dimensional Lévy processes is studied under certain regular
variation conditions on the Lévy-Khinchin exponent and the Lévy measure.
This is a joint work with Kouji Yano (Osaka).
- 2025/11/18(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
鎌谷 研吾(統計数理研究所)
Fluid limit of piecewise deterministic Monte Carlo methods
跳ね返り粒子サンプラーやジグザグサンプラーなどの区分決定的マルコフ過程を用いたモンテカルロ法は，従来のMCMCの連続時間版として注目されている．本研究では，凸ポテンシャル下での遷移過程，すなわち低確率領域から高確率領域への動きを解析する．生成子を速い・遅い成分に分けて解析し，速い成分は非エルゴード的だが，遅い成分が再活性化を担うことで安定的な振る舞いが導かれることがわかった．
これらの結果は，大規模なモデルでの区分確定的マルコフ過程を用いたモンテカルロ法の理論的・実践的示唆を与える．
本研究は，S. Agrawal, J. Bierkens, G. O. Robertsとの共同研究．
- 2025/11/11(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Ciprian A. Tudor (Université de Lille 1)
Stein-Malliavin calculus and asymptotic independence
We will present a generalization of the Stein-Malliavin
calculus that allows to quantify the asymptotic independence. We will
also discuss the applications of this method to several well-known
limit theorems and to statistical inference.
- 2025/10/21(Tue) 確率論セミナー
15:10--16:20 数学教室 大セミナー室(E404) (ダブルヘッダーのため，通常とは時間帯が異なります)
Chiara Franceschini(Università di Modena e Reggio Emilia)
Integrable models of non-equilibrium: duality relations and invariant measure
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory.
This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
- 2025/10/21(Tue) 確率論セミナー
16:30--17:40 数学教室 大セミナー室(E404)
Patrícia Gonçalves(Instituto Superior Técnico)
The boundary driven zero-range process
In this talk I will present the hydrodynamic limit and stationary fluctuations of the zero-range process with open boundary. Contrarily to the boundary driven exclusion the non equilibrium stationary state (NESS) of the zero range process is a product measure though not translation invariant. I will assume that the model is attractive and the initial state is stochastically dominated by the NESS. I will also make the comparison with the exclusion process and explain in detail the most challenging technical problems in deriving the proofs.
- 2025/10/14(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
針谷 祐(東北大学)
Invariance of three-dimensional Bessel bridges in terms of time reversal
Given three real numbers $a, b$ and $t$ with $t$ positive, let $\beta$ be a
one-dimensional Brownian bridge of length $t$ from $a$ to $b$. In this talk,
based on a conditional identity in law between Brownian bridges stemming from
Pitman's theorem, we show that the process given by
\[
\beta_{t-s}+\biggl| b-a+
\min _{0\le u\le t-s}\beta_{u}-\min _{t-s\le u\le t}\beta_{u}
\biggr|
-\biggl|
\min _{0\le u\le t-s}\beta_{u}-\min _{t-s\le u\le t}\beta_{u}
\biggr|
\]
for $0 \le s \le t$, has the same law as $\beta$. The path transformation
that describes the above process is proven to be an involution, commute with
time reversal, and preserve a Pitman-type transformation in conjunction with
time reversal. Since it does not change the minimum value in particular,
the transformation also preserves the law of a three-dimensional Bessel bridge
of length $t$. As an application, some distributional invariances of three-dimensional
Bessel processes are derived. This talk is based on arXiv:2503.06813.
- 2025/10/7(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Beatriz Salvador(Instituto Superior Técnico)
From duality to correlations
The characterization of non-equilibrium fluctuations in boundary-driven interacting particle systems (IPS) is, in general, a challenging problem. Much of the difficulty arises from the lack of effective tools to estimate the centered correlation functions of such systems.
In this talk, I will present an approach based on stochastic duality to derive bounds on the k-point centered correlation functions of an IPS that possesses a suitable duality property and a specific class of duality function. We will discuss in detail how this method applies to three toy models: the symmetric simple partial exclusion process SEP($\alpha$), the symmetric simple inclusion process SIP($\alpha$), and the independent random walkers IRW, all considered with open boundaries. The case $k=2$ for SEP($\alpha$) is joint work with Chiara Franceschini, Patrícia Gonçalves, and Milton Jara [1], while the general case is part of ongoing work with Patrícia Gonçalves and Augusto Teixeira.
References:
[1] Franceschini, C., Gonçalves, P., Jara, M., Salvador, B. (2024): Non-equilibrium fluctuations for SEP($\alpha$) with open boundary, Stochastic Processes and their Applications, Volume 178, 104463.
[2] Gonçalves, P. and Salvador, B. (2024) On the correlations of some microscopic random systems. ArXiv preprint
https://arxiv.org/abs/2410.17926.
- 2025/7/29(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
大井 拓夢(東京理科大学)
Homeomorphism of the Revuz correspondence for finite energy integrals
ディラック測度と局所時間の対応など、smooth measureと正値連続加法的汎関数(PCAF)の一対一対応 (Revuz対応) が知られている。本講演では有限エネルギーを持つクラスに制限したRevuz対応が同相写像になることを述べる。ただし、有限エネルギーの smooth measure 全体の空間には西森-土田-富﨑-上村(2024+)により導入されたディリクレ形式から誘導される自然な距離を考え、有限エネルギーのPCAF全体の空間には、局所一様位相の下で $L^2(P_{m+\kappa+\nu_0})$-収束を考える。ここで$m$はディリクレ形式の基礎になる測度、$\kappa$ はkilling measure、$\nu_0$は連続的に死滅する場合に相当する汎関数である。
- 2025/7/22(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Hugo Da Cunha(Université Lyon 1)
Boundary effects in the Facilitated Exclusion Process
The Facilitated Exclusion Process (FEP) is a model of stochastic interacting particle system whose dynamics is subject to kinetic constraints, leading to a phase transition at the critical density 1/2: under this threshold, the system is completely frozen. In recent years, the FEP has been extensively studied on the periodic setting, but in this talk I will consider it with boundary conditions. I will focus first on open boundaries, with particles reservoirs at both ends allowing creation/annihilation of particles. If time allows, I will also consider the case of closed boundaries, when there are impermeable walls at both ends.
At the macroscopic level, the boundary dynamics impose some boundary conditions on the PDE describing the hydrodynamic limit, that can be of different types (such as Dirichlet, Neumann or Robin). These boundary conditions are not standard as they differ from what is usually found in other exclusion processes, and this is due to the two-phased nature of FEP.
This talk is based on joint works with Clément Erignoux, Marielle Simon and Lu Xu.
- 2025/7/15(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Lu Wei(Texas Tech University)
Cumulant Structures of Entanglement Entropy
We discuss new methods to, in principle, obtain all
cumulants of von Neumann entropy over different models of random
states. The new methods uncover the structures of cumulants in terms
of lower-order joint cumulants involving families of ancillary linear
statistics. Importantly, the new methods avoid the task of simplifying
nested summations when using existing methods in the literature that
becomes prohibitively tedious as the order of cumulant increases. This
talk is based on a joint work with Youyi Huang (arXiv: 2502.05371).
- 2025/6/17(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Johannes Ruf(London School of Economics)
Predictable variations in stochastic calculus
The focus of this talk is the transformation of increments of a
stochastic process by a predictable function. Many operations in
stochastic analysis can be considered under this point of view.
Stochastic integrals, for example, are linear functionals of process
increments. Although mathematically equivalent, focusing on
transformation of increments often leads to simpler proofs of more
general statements in stochastic calculus. In this talk specifically, we
illustrate how considering predictable variations lead to various
Ito-type formulas.
Joint work with Ales Cerny
- 2025/5/20(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Evangelos A. Nikitopoulos(University of Michigan)
Noncommutative stochastic calculus and SDEs
Noncommutative or free probability is a branch of mathematics that is useful for describing the large-
$N$ limits of many $N \times N$ random matrix models. In this theory, classical probability spaces are replaced by pairs
$(\mathcal{A},\tau)$, where $\mathcal{A}$ is an (operator) algebra and $\tau:\mathcal{A} \to \mathbb{C}$ is a certain kind of linear functional. In such a pair,
$\mathcal{A}$ and $\tau$ are conceptualized as the space of ``noncommutative random variables'' and the ``expectation'' functional on
$\mathcal{A}$, respectively. The analogy with classical probability goes much further. Indeed, there are notions of distribution, independence, $L^p$ spaces, conditional expectation, and more. My talk will focus on my joint work with David Jekel and Todd Kemp on developing a general noncommutative theory of stochastic calculus and SDEs.
- 2025/5/13(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
笹谷 晃平(東京大学)
Construction of p-energy measures associated with strongly local p-energy forms
p-エネルギー形式とは，”Dirichlet形式のL^p版”にあたる対象であり，近年その構成及び性質の研究が進展している.（主たる動機の一つは、フラクタル上に(1,p)-Sobolev空間の対応物を構成することにある．）正則なDirichlet形式に対しては，その局所化にあたるエネルギー測度を定めることができるが，p-エネルギー形式の場合には同様の構成法を適用することが困難であり，エネルギー測度はエネルギー形式の具体的な表現や，自己相似性の仮定に強く依存する形で個別に構成されていた．講演者は，強局所，正則なDirichlet形式に対応する条件のみを課したp-エネルギー形式に対し，(空間/エネルギーの自己相似性の仮定を必要とせず)，Dirichlet形式の場合とは異なったアプローチにより対応するエネルギー測度を構成し，連鎖律，Leibniz則などの諸性質や，それらの性質を満たすエネルギー測度の一意性を示した(arXiv:2502.13069)．本講演では，これらの研究背景及び結果をより詳しく紹介する．
- 2025/4/22(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Mikhail Zhitlukhin(Steklov Mathematical Institute)
Evolutionary models of asset markets
This talk explores evolutionary models of asset markets in mathematical
finance, in which many interacting agents compete for capital. We focus
on the asymptotic dynamics of such systems—particularly which strategies
accumulate wealth faster than others. A key feature of our approach is
the existence of strategies that outperform others irrespective of
competing agents' behavior, influencing the market's long-term
characteristics. Unlike traditional models, we examine endogenous price
formation, offering a new perspective on market evolution. I will review
foundational and recent results, highlighting insights into strategy
dominance and market dynamics.
- 2025/4/15(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E404)
Jim Gatheral(Baruch College, CUNY)
The SSR under Quadratic Rough Heston
We extend the hybrid scheme of Gatheral (2022) and apply the finite difference methodology of Bourgey et al. (2024) to compute the skew-stickiness ratio (SSR) under quadratic rough Heston. We find that the quadratic rough Heston model not only provides good joint fits to both SPX and VIX volatility smiles but also produces credible SSR values, whilst remaining extremely parsimonious. By examining the historical evolution of the quadratic rough Heston model, and relating it to well-known classical stochastic volatility models, we can begin to understand the underlying reasons for its seemingly unreasonable effectiveness.
- 2025/4/1(Tue) 確率論セミナー
15:10--16:40 数学教室 大セミナー室(E301)(普段の教室と異なります)
José Luis Pérez Garmendia(CIMAT)
Universality classes for general random matrix flows
In this talk, we consider matrix-valued processes described as solutions
to stochastic differential equations of a very general form. We study
the family of empirical measure-valued processes constructed from the
corresponding eigenvalues. We show that this family, indexed by the size
of the matrix, is tight under very mild assumptions on the coefficients
of the initial SDE. We characterize the limiting distributions of its
subsequences as solutions to an integral equation.
Using this result, we explore certain universality classes of random
matrix flows, which generalize classical results related to Dyson
Brownian motion and squared Bessel particle systems. We also identify
new phenomena, such as the existence of generalized Marchenko-Pastur
distributions supported on the real line. Additionally, we introduce
universality classes associated with generalized geometric matrix
Brownian motions and Jacobi processes. Finally, under certain
conditions, we study the convergence of the empirical measure-valued
process of eigenvalues associated with matrix flows to the law of a free
diffusion.