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Kohei Suzuki

Publications and source records attributed to Kohei Suzuki.

At least 19 recordsLinked to original sources
arXiv2026

Spectral gap for unlabelled Ginibre Interacting Brownian motion

We determine the exact spectral gaps for both the finite-particle and infinite-particle unlabelled Ginibre interacting Brownian motions. In every finite-particle system, the spectral gap is equal to one, whereas for the infinite-particle system it is equal to two. The infinite-particle dynamics therefore has a strictly larger spectral gap than any of its finite-particle counterparts, revealing an enhancement of spectral gaps in the passage from finite to infinite particle systems.

math.PR↗
arXiv2026

Pyramids and Extended Metric Measure Spaces

A pyramid is a generalisation of metric measure spaces (mm-spaces) introduced by M.~Gromov (Birkh\"auser 1999) to establish a geometric framework for measure-concentration problems. An extended metric measure space (emm-space) is another generalisation of mm-spaces introduced by Ambrosio--Gigli--Savar\'e (Invent.~Math.~2014) to extend Sobolev calculus and optimal transport theory to a broader extent. We prove that every pyramid has a representation by an emm-space through $1$-Lipschitz order. Furthermore, if pyramids are concentrated, this correspondence is unique up to isomorphism. This shows, for the first time, that all pyramids can be realised by concrete geometric spaces. Based on this representation, we introduce a new notion, a concentrated emm-space. We then define the observable distance for concentrated emm-spaces and establish three equivalent characterisations of concentration in terms of pyramids, Lipschitz observables and the observable distance. Furthermore, by developing an fibration approach, we show the $\Gamma$-$\limsup$ inequality of Cheeger energies as well as the stability of the log-Sobolev inequality and the Poincar\'e inequality under the weak convergence of pyramids associated with emm-spaces. Our results provide a new geometric approach for studying both the convergence of emm-spaces and concentration-of-measure phenomena across a broad class of infinite-dimensional models that have so far remained largely beyond the reach of existing geometric methods. Many of the significant examples arise in probability theory, including the Wiener space, the configuration space, Gaussian fields such as massive Gaussian free fields, spatial white noise and massive bi-Laplacian fields.

math.MG↗
arXiv2026

Collision and non-collision for diffusions on configuration space

We develop criteria for collision and non-collision of reversible infinitely many interacting diffusion processes in the real line. The approach is potential-theoretic and is based on capacity estimates for symmetric Dirichlet forms on the configuration space. Our main results are model-independent in the sense that no determinantal or Pfaffian structure, prescribed interaction potential, or explicit labelled stochastic differential equation is required. The non-collision criterion involves only the second and third correlation functions of the reversible measure, whereas the collision criterion is based on a local lower bound for a finite-volume conditional density of the reversible measure. As an application, we identify the sharp collision threshold for the diffusion associated with the $\mathsf{Sine}_\beta$-symmetric Dirichlet form: the collision set is polar if and only if $\beta\ge 1$. This provides an infinite-particle counterpart of the classical collision threshold for the finite-particle Dyson Brownian motion with inverse temperature $\beta$.

math.PR↗
arXiv2026

A Real-Time Remote-Sensing-Guided Decision-Support Framework for Cloud-Seeding Operations: A Field Demonstration Using Himawari-9 and C-band Phased Array Weather Radar

This study proposes a real-time remote-sensing-guided decision-support framework for cloud-seeding operations using high frequency geostationary satellite and ground weather radar observations. The framework integrates cloud assessment, human-in-the-loop decision support, and aircraft operation to translate high-frequency remote-sensing information into actionable guidance for seeding aircraft. We demonstrate the framework using 2.5-min Himawari-9 geostationary satellite observations and 60-s C-band phased-array weather radar (C-PAWR) observations during the preliminary dry-ice cloud-seeding field campaign conducted over Toyama Bay, Japan, in January 2026. In the 13 January case, the framework enabled the ground team to identify a developing cumulus cloud with a lifetime of approximately 20 min, communicate guidance to the aircraft, and conduct seeding immediately before the cloud began to dissipate naturally. Candidate seedable clouds were identified from Himawari-9 infrared indices, and their selection was supported by near-real-time C-PAWR observations of precipitation echoes. Because the released dry-ice amount was limited to 30 kg, this study does not attempt to attribute subsequent cloud evolution to seeding effects. Instead, the results demonstrate that rapid-scan satellite and ground radar observations can support real-time target selection and aircraft guidance for responsible, operationally feasible weather-intervention field experiments.

physics.ao-ph↗
arXiv2026

Brownian motion in Minkowski normed spaces

A Minkowski normed space is the Euclidean space equipped with a (possibly asymmetric) uniformly convex and smooth norm, forming a particular class of Finsler manifolds. We construct a stochastic process with one-dimensional time marginal densities given by the fundamental solution to the nonlinear Finsler heat equation in Minkowski normed spaces. This process is constructed as a solution to a singular McKean--Vlasov stochastic differential equation and constitutes a nonlinear Markov process in the sense of McKean. Furthermore, we show that solutions to this stochastic differential equation are pathwise unique, and thus probabilistically strong solutions, though the equation has singular coefficients beyond the subcritical regime. Since our construction is a natural extension of the construction of standard Brownian motion from the standard heat kernel, we call this process \emph{Brownian motion in Minkowski normed spaces.} To the best of our knowledge, this is the first construction of stochastic processes associated with nonlinear heat equation in Finslerian spaces.

math.PR↗
arXiv2026

Stability of Synthetic Ricci Curvature Lower Bounds for Inverse Limit Extended Metric Measure Spaces

We show that every Polish extended metric measure space arises as an inverse limit of metric measure spaces up to isomorphism. We then prove that synthetic Ricci curvature lower bounds and several functional inequalities, including the log-Sobolev, Talagrand, Poincar\'e, and dimension-free Harnack inequalities are stable under inverse limit. We discuss applications to infinite-dimensional spaces, including abstract Wiener spaces and their quotient spaces.

math.FA↗
arXiv2026

Simulated Annealing for Quadratic and Higher-Order Unconstrained Integer Optimization

Simulated annealing (SA) is a key algorithm for solving combinatorial optimization problems, which model numerous real-world systems. While SA is commonly used to solve quadratic unconstrained binary optimization (QUBO) problems, many practical problems are more naturally formulated using integer variables. We therefore study quadratic and higher-order unconstrained integer optimization (QUIO and HUIO) problems, which generalize QUBO by allowing integer-valued variables and higher-order interactions. Conventional approaches often convert these problems into QUBO formulations through binary encoding and the reduction of higher-order terms. Such conversions, however, greatly increase the number of variables and interactions, resulting in long computation times and, for large-scale problems, even making the conversion itself a dominant computational bottleneck. To overcome this limitation, we propose an efficient framework that directly applies SA to QUIO and HUIO problems without converting them into QUBO. Within this framework, we introduce an optimal-transition Metropolis method, designed to improve efficiency when the variable range is wide, and evaluate its performance alongside the conventional Metropolis and heat bath methods. Numerical experiments demonstrate that the proposed direct approach achieves higher efficiency and better solution quality than the conventional QUBO-based formulation and reveal the practical advantages of the optimal-transition Metropolis method. The algorithm developed in this study is available as part of the open-source library OpenJij, which provides a Python front end with a C++ backend.

cond-mat.stat-mech↗
arXiv2026

Hidden low-discrepancy structures in random point sets

We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the number of geometric patterns for $(0, m, d)$-nets in base $b$. By applying the elementary probability bounds together with this counting result, we then give scaling conditions on $N$ as a function of $m$ such that this probability converges to $1$ and $0$, respectively.

math.CO↗
arXiv2025

Infinite Interacting Brownian Motions and EVI Gradient Flows

We give a sufficient condition under which the time-marginal law of $μ$-reversible infinite interacting Brownian motions is characterised as the steepest gradient descent of the relative entropy in the Wasserstein space in the sense of evolution variational inequality (EVI). This is an infinite-dimensional generalisation of Jordan-Kinderlehrer-Otto/Ambrosio-Gigli-Savaré theory. Consequently, the configuration space (the space of locally finite point measures) endowed with the reversible measure $μ$ is an RCD space and the time-marginal law is identified to the heat flow on this space. Our result covers the infinite-dimensional Dyson Brownian motion with bulk and soft-edge limits; the latter yields Airy line ensemble as its stationary process, a central object in KPZ universality. Our result therefore provides an optimal transport characterisation of these models as Wasserstein gradient flows, and establishes a range of new functional inequalities (HWI, distorted Brunn-Minkowski, dimension-free Harnack and many others) as a corollary. As an application, we discover the new phenomena, dynamical number rigidity and dynamical tail triviality, that the time-marginal law possesses number rigidity and tail triviality for every time $t>0$, revealing a propagation of random crystal and extremal structures by the Dyson Brownian motions.

math.PR↗
arXiv2025

First-order nuclear dipolar order in rotating solids

Nuclear spins' dipolar order is created under magic angle spinning through the first-order process made possible by simultaneous implementation of dipolar recoupling and adiabatic demagnetization in a reference frame reached out through nested transformations, firstly from the laboratory frame into the rotating frame, and then into the spin coordinate system nutating inside its parent frame. In such a nutating frame, both the static and resonantly rotating radio-frequency (RF) fields are invisible, and the re-introduced dipolar interaction provides a secular eigenstate on which dipolar order develops with assist of an additional portion of RF field designed to implement adiabatic demagnetization in the nutating frame.

quant-ph↗
arXiv2025

Quantum Annealing with Qubit-Resonator Systems for Simultaneous Optimization of Binary and Continuous Variables

Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases, the cost function may also involve continuous variables. Representing continuous variables using quantum bits requires binary encoding, which demands a large number of qubits. To overcome this limitation, an approach using quantum resonators has been proposed, enabling the direct handling of continuous variables within the quantum annealing framework. On the other hand, certain optimization problems involve both binary and continuous variables simultaneously, and a quantum annealing method capable of efficiently solving such hybrid problems has not been established. Here, we propose a quantum annealing method based on a hybrid system composed of qubits and resonators, aiming to minimize cost functions that contain both binary and continuous variables. We present a general framework for hybrid quantum annealing using such systems, and investigate its feasibility and effectiveness through numerical simulations.

quant-ph↗
arXiv2025

A phase transition in the Bakry-Émery gradient estimate for Dyson Brownian motion

In this paper, we find a gap between the lower bound of the Bakry-Émery $N$-Ricci tensor ${\rm Ric}_N$ and the Bakry-Émery gradient estimate ${\sf BE}$ in the space associated with the finite-particle Dyson Brownian motion (DBM) with inverse temperature $0<β<1$. Namely, we prove that, for the weighted space $(\mathbb R^n, w_β)$ with $w_β=\prod_{i<j}^n |x_i-x_j|^β$ and any $N\in[n+\fracβ{2}n(n-1),+\infty]$, $β\ge 1 \implies {\rm Ric}_N \ge 0 \ \& \ {\sf BE}(0,N)$ hold; $0 < β< 1 \implies {\rm Ric}_N \ge 0$ holds while ${\sf BE}(0,N)$ does not, which shows a phase transition of the Dyson Brownian motion regarding the Bakry-Émery curvature bound in the small inverse temperature regime.

math.PR↗
arXiv2025

Curvature bound of Dyson Brownian Motion

We construct a strongly local symmetric Dirichlet form on the configuration space $Υ$ whose symmetrising (thus also invariant) measure is $\mathsf{sine}_β$, which is the law of the sine $β$ ensemble for every $β>0$. For every $β>0$, this Dirichlet form satisfies the Bakry-Émery gradient estimate $\mathsf{BE}(K, \infty)$ with $K=0$. This implies various functional inequalities, including the local Poincaré inequality, the local log-Sobolev inequality and the local hyper-contractivity. We then introduce an $L^2$-transportation-type extended distance $\bar{\sf d}_Υ$ on $Υ$, and prove the dimension-free Harnack inequality and several Lipschitz regularisation estimates of the $L^2$-semigroup associated with the Dirichlet form in terms of $\bar{\sf d}_Υ$. As a result of $\mathsf{BE}(0,\infty)$, we obtain that the dual semigroup on the space of probability measures over $Υ$, endowed with a Benamou--Brenier-like extended distance $\mathsf{W}_{\mathcal E}$, satisfies the evolutional variation inequality with respect to the Bolzmann--Shannon entropy $\mathsf{Ent}_{\mathsf{sine}_β}$ associated with $\mathsf{sine}_β$. Furthermore, the dual semigroup is characterised as the unique $\mathsf{W}_{\mathcal E}$-gradient flow in the space of probability measures with respect to $\mathsf{Ent}_{\mathsf{sine}_β}$. Finally, we provide a sufficient condition for $\mathsf{BE}(K, \infty)$ beyond $\mathsf{sine}_β$ and apply it to the infinite particle diffusion whose symmetrising measure is the law of the $1$-dimensional $(β,s)$-circular Riesz gas with $β>0$ and $0<s<1$.

math.PR↗
arXiv2025

BV Functions and Sets of Finite Perimeter on Configuration Spaces

This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space $\mathbb R^n$ equipped with the Poisson measure $π$. We first provide a rigorous meaning and construction of the $m$-codimensional Poisson measure -- formally written as "$(\infty-m)$-dimensional Poisson measure" -- on the configuration space. We then show that our construction is consistent with potential analysis by establishing the absolute continuity with respect to Bessel capacities. Secondly, we introduce three different definitions of BV functions based on the variational, relaxation and the semigroup approaches, and prove the equivalence of them. Thirdly, we construct perimeter measures and introduce the notion of the reduced boundary. We then prove that the perimeter measure can be expressed by the $1$-codimensional Poisson measure restricted on the reduced boundary, which is a generalisation of De Giorgi's identity to the configuration space. Finally, we construct the total variation measures for BV functions, and prove the Gauß--Green formula.

math.MG↗
arXiv2025

Integral Varadhan formula for non-linear heat flow

We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do not assume the reversibility of the metric, and the distance function can be asymmetric. In this generality, we reveal that the probabilistic interpretation is well-suited for our formula; the probability that a particle starting from a set $A$ can be found in another set $B$ describes the distance from $A$ to $B$. One side of the estimates (the upper bound of the probability) is also established in the nonsmooth setting of infinitesimally strictly convex metric measure spaces satisfying the local Sobolev-to-Lipschitz property.

math.PR↗
arXiv2025

Spin-$S$ Ising models with multispin interactions on the one-dimensional chain and two-dimensional square lattice

We study spin-$S$ Ising models with $p$-spin interactions on the one-dimensional chain and the two-dimensional square lattice. Here, $S$ denotes the magnitude of the spin and $p$ represents the number of spins involved in each interaction. The analysis is performed for $S=1/2,1,3/2,2$ and $p=3,4,5$. For the one-dimensional model, we formulate transfer matrices, and numerically diagonalize them to analyze the temperature dependence of the free energy and spin-spin correlations. In the case of $S=1/2$, the free energy does not depend on $p$, and the spin-spin correlations are uniformly enhanced across all temperature scales as $p$ increases. In contrast, for $S \geq 1$, the free energy varies with $p$, and the spin-spin correlations are significantly enhanced at lower temperatures as $p$ increases. For the two-dimensional model, by using multicanonical simulations, we analyze physical quantities such as an order parameter, internal energy, and specific heat. In addition, we define and examine an order parameter to distinguish ordered and disordered phases. It is found that a first-order phase transition occurs at finite temperatures for all $S$ and $p\geq3$, and increasing $p$ strengthens its nature. We present $S$ and $p$ dependence of the transition temperature and latent heat, and discuss effects of higher-order interactions on the nature of phase transitions.

cond-mat.stat-mech↗
arXiv2024

Buffer gas cooling of carbon atoms

We demonstrate buffer gas cooling of carbon atoms to cryogenic temperatures. By employing pulsed two-photon excitation followed by vacuum ultraviolet fluorescence detection, we measured the arrival time distribution of the ablated carbon atoms to the detection volume at various helium buffer gas densities. The experimental data, corroborated by Monte Carlo simulations, reveal a rapid decrease in the local temperature of the carbon atom gas to approximately 10~K within tens of microseconds. The findings establish a major step towards novel research utilizing cold and ultracold carbon atoms.

physics.atom-ph↗