arXiv subjects

Masato Hisakado

Publications and source records attributed to Masato Hisakado.

At least 19 recordsLinked to original sources

arXiv2026

Bulk Phase Transition and Edge Behavior in Temporally Correlated Random Matrices

We study long-range correlated Wigner-type matrices built from row-independent stationary Gaussian sequences. For exponentially decaying (AR(1)) correlations, the bulk spectral density deforms from the semicircle law via an explicit combinatorial "hub" mechanism, yet we verify the flatness and decay hypotheses of the matrix-Dyson-equation framework (MDE), with numerical evidence supporting Tracy-Widom edge universality for every fixed $\rho<1$ of the exponential decay correlations; the degenerate limit $\rho\to1^-$ reduces to a symmetrized Volterra operator, connecting to the singular-value cascade identified in a companion BBP analysis. For power-law correlations $dt\sim t^{-\gamma}$, we identify $\gamma_c=1/2$ as the critical point for divergence of the bulk fourth-moment, while $\gamma=1$ marks the breakdown of the flatness condition governing the MDE edge analysis. We prove the fourth-moment transition exactly and find numerically that the self-consistent edge varies smoothly across $\gamma=1$, with no evidence of a kink or discontinuity.

cond-mat.stat-mech↗

arXiv2026

A Cascade of Volterra-Operator BBP Transitions in a Correlated Wigner Matrix

We study a Wigner-type random matrix in which the off-diagonal correlation between entries is generated by a random factor shared among all entries in a given row and column, with the coupling strength held fixed as the matrix size grows. Although the bulk spectral moments remain those of the pure semicircle law, we show that the underlying correlation matrix decomposes into a vanishing bulk together with a countable family of outlier eigenvalues that, at fixed rank $k$, converge to the singular values of a compact Volterra (cumulative-sum) integral operator -- obtained in closed form via the classical Karhunen--Lo\`eve expansion of Brownian motion and confirmed numerically to better than one percent across the top twenty such values. Each singular value drives an independent Baik--Ben Arous--P\'{e}ch\'{e} (BBP) transition as the coupling strength increases, producing an evenly spaced, discrete hierarchy of critical points -- rather than a single transition -- at each of which one further eigenvalue detaches from the semicircle edge, in close agreement with direct diagonalization. We show that this mechanism generalizes to a broader family of correlation structures, with the critical hierarchy in every case set by the spectrum of an associated compact integral operator.

cond-mat.stat-mech↗

arXiv2026

Temporal Coarse-Graining of Multi-Sector Default Count Data Generates Posterior-Implied Copulas

Sectoral default dependence is usually described by a static correlation matrix, a static copula, or a small number of common factors. Such representations, when specified separately at each observation horizon, do not by themselves explain why the effective dependence observed in monthly credit data differs from that observed after annual aggregation. This paper proposes a dynamic low-rank state-space model for monthly multi-sector default-count data and studies the dependence structure induced by temporal coarse-graining. The leading eigenvectors of the monthly sectoral default-rate correlation matrix are used as fixed loading directions for persistent AR(1) latent credit-state factors, and defaults are modeled through a binomial observation layer. Survival aggregation of monthly posterior probability paths induces horizon-dependent distributions of sectoral default-probability vectors, from which effective correlation matrices, eigenvalue spectra, and posterior-implied rank copulas are obtained. Applied to S\&P monthly sector-level default-count data from 1981--01 to 2021--09, a two-factor specification captures the dominant market-wide and sector-rotation modes, reproduces the annual amplification of the leading eigenvalues, and generates heterogeneous copula structures across sector pairs. In an annual forecast evaluation, the dynamic factor specifications reduce the under-dispersion of static binomial and beta-binomial baselines, improving interval coverage and CRPS for aggregate portfolio counts. In log-score-based forecast comparisons, the one-factor specification is highly competitive, whereas the two-factor specification improves sector-level calibration as measured by per-sector CRPS.

q-fin.RM↗

arXiv2025

Deformation of semi-circle law for the correlated time series and Phase transition

We study Wigner-type random matrices constructed from financial time series with temporal correlations. We characterize the deformed spectral law through its moments and observe behavior consistent with a modified semicircle law. We apply our framework to several financial time series and observe deviations from the semicircle law in specific foreign exchange markets. The difference from the semicircle law for the financial time series depends on the temporal correlation of financial time series. We provide a moment analysis for both exponential and power law correlation structures and show that the fourth moment increases with the strength of correlations. In the case of power law decay, a transition emerges between regimes with finite and divergent higher-order moments. Finally, numerical simulations support the analytical predictions and reveal finite-size scaling behavior near the transition.

cond-mat.stat-mech↗

arXiv2025

Phase transition in a long-memory log-Gaussian Cox process

We study a stochastic point process with power-law temporal correlations driven by hidden variables. We show that a generalized Merton-type model under an exponential-tail asset assumption, obtained by replacing the Gaussian cumulative distribution function with a logistic CDF, together with an appropriate double-scaling limit, converges to a log-Gaussian Cox process (LGCP) with log-normal intensity. The resulting LGCP exhibits a phase transition at the critical power index $\gamma=1$. This transition separates regimes of short-memory dynamics from long-memory behavior characterized by anomalous diffusion. We further demonstrate that temporal correlations persist even in the Poisson limit when the scaling is properly defined, in contrast to conventional Poisson convergence where memory effects vanish. We also compare this LGCP with self-exciting processes such as Hawkes processes, highlighting fundamental differences in correlation structure and extreme-event behavior. The theoretical results are illustrated using credit risk time series, and empirical estimation of the temporal correlation parameter from historical default data provides evidence for long-memory behavior in pre-1980 credit portfolios.

q-fin.RM↗

arXiv2024

Structural Properties of the Asymmetric Barab\'asi-Albert Model in the Lattice Limit

The Asymmetric BA model extends the Barab\'asi-Albert scale-free network model by introducing a parameter $\omega$. As $\omega$ varies, the model transitions through different network structures: an extended lattice at $\omega = -1$, a random graph at $\omega = 0$, and the original scale-free network at $\omega = 1$. We derive the exact degree distribution for $\omega = -r/(r+k)$, where $k \in \{0,1,\cdots\}$, and develop a perturbative expansion around these values of $\omega$. Additionally, we show that for $\omega = -1 + \varepsilon$, the clustering coefficient scales as $\ln t / \sqrt{\varepsilon} t$ and approaches zero as $t \to \infty$, confirming the absence of small-world properties.

cond-mat.stat-mech↗

arXiv2024

$\alpha$ Annealing of Ant Colony Optimization in the infinite-range Ising model

Ant colony optimization (ACO) leverages the parameter $\alpha$ to modulate the decision function's sensitivity to pheromone levels, balancing the exploration of diverse solutions with the exploitation of promising areas. Identifying the optimal value for $\alpha$ and establishing an effective annealing schedule remain significant challenges, particularly in complex optimization scenarios. This study investigates the $\alpha$-annealing process of the linear Ant System within the infinite-range Ising model to address these challenges. Here, "linear" refers to the decision function employed by the ants. By systematically increasing $\alpha$, we explore its impact on enhancing the search for the ground state. We derive the Fokker-Planck equation for the pheromone ratios and obtain the joint probability density function (PDF) in stationary states. As $\alpha$ increases, the joint PDF transitions from a mono-modal to a multi-modal state. In the homogeneous fully connected Ising model, $\alpha$-annealing facilitates the transition from a trivial solution at $\alpha=0$ to the ground state. The parameter $\alpha$ in the annealing process plays a role analogous to the transverse field in quantum annealing. Our findings demonstrate the potential of $\alpha$-annealing in navigating complex optimization problems, suggesting its broader application beyond the infinite-range Ising model.

cond-mat.stat-mech↗

arXiv2023

Deformation of Marchenko-Pastur distribution for the correlated time series

We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution (MPD) in the double scaling limit. When there is temporal correlation, the eigenvalue distribution converges to the deformed MPD which has a longer tail and higher peak than the MPD. Here we discuss the moments of distribution and convergence to the deformed MPD for the Gaussian process with a temporal correlation. We show that the second moment increases as the temporal correlation increases. When the temporal correlation is the power decay, we observe a phenomenon such as a phase transition. When $\gamma>1/2$ which is the power index of the temporal correlation, the second moment of the distribution is finite and the largest eigenvalue is finite. On the other hand, when $\gamma\leq 1/2$, the second moment is infinite and the largest eigenvalue is infinite. Using finite scaling analysis, we estimate the critical exponent of the phase transition.

cond-mat.stat-mech↗

arXiv2023

Information cascade on networks and phase transitions

Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barab\'{a}si-Albert(BA) model, and lattice networks -- by using one parameter $\omega$; $\omega=1,0, -1$ respectively correspond to these networks. $\omega$ is related to the size of hubs. We discuss the differences between the phases in which the networks depend. In $\omega\ne -1$, without, the following two types of phase transitions can be observed: information cascade transition and super-normal transition. The first is the transition between a state where most voters make correct choices and a state where most of them are wrong. This is an absorption transition that belongs to the non-equilibrium transition. In the symmetric case, the phase transition is continuous and the universality class is the same as nonlinear P\'{o}lya model. In contrast, in the asymmetric case, there is a discontinuous phase transition, where the gap depends on the network. The super-normal transition is the transition of the convergence speed, and the critical point of the convergence speed transition depends on $\omega$. At $\omega=1$, in the BA model, this transition disappears. Both phase transitions disappear at $\omega=-1$ in the lattice case. In conclusion, as the performance near the lattice case, $\omega\sim-1$ exhibits the best performance of the voting in all networks. As the hub size decreases, the performance improves.

physics.soc-ph↗

arXiv2023

Self-exciting negative binomial distribution process and critical properties of intensity distribution

We study the continuous time limit of a self-exciting negative binomial process and discuss the critical properties of its intensity distribution. In this limit, the process transforms into a marked Hawkes process. The probability mass function of the marks has a parameter $\omega$, and the process reduces to a "pure" Hawkes process in the limit $\omega\to 0$. We investigate the Lagrange--Charpit equations for the master equations of the marked Hawkes process in the Laplace representation close to its critical point and extend the previous findings on the power-law scaling of the probability density function (PDF) of intensities in the intermediate asymptotic regime to the case where the memory kernel is the superposition of an arbitrary finite number of exponentials. We develop an efficient sampling method for the marked Hawkes process based on the time-rescaling theorem and verify the power-law exponents.

math.PR↗

arXiv2022

Multi-Dimensional self-exciting NBD process and Default portfolios

In this study, we apply a multidimensional self-exciting negative binomial distribution (SE-NBD) process to default portfolios with 13 sectors. The SE-NBD process is a Poisson process with a gamma-distributed intensity function. We extend the SE-NBD process to a multidimensional process. Using the multidimensional SE-NBD process (MD-SE-NBD), we can estimate interactions between these 13 sectors as a network. By applying impact analysis, we can classify upstream and downstream sectors. The upstream sectors are real-estate and financial institution (FI) sectors. From these upstream sectors, shock spreads to the downstream sectors. This is an amplifier of the shock. This is consistent with the analysis of bubble bursts. We compare these results to the multidimensional Hawkes process (MD-Hawkes) that has a zero-variance intensity function.

q-fin.RM↗

arXiv2021

From the multi-terms urn model to the self-exciting negative binomial distribution and Hawkes processes

This study considers a new multi-term urn process that has a correlation in the same term and temporal correlation. The objective is to clarify the relationship between the urn model and the Hawkes process. Correlation in the same term is represented by the P\'{o}lya urn model and the temporal correlation is incorporated by introducing the conditional initial condition. In the double-scaling limit of this urn process, the self-exciting negative binomial distribution (SE-NBD) process, which is a marked Hawkes process, is obtained. In the standard continuous limit, this process becomes the Hawkes process, which has no correlation in the same term. The difference is the variance of the intensity function in that the phase transition from the steady to the non-steady state can be observed. The critical point, at which the power law distribution is obtained, is the same for the Hawkes and the urn processes. These two processes are used to analyze empirical data of financial default to estimate the parameters of the model. For the default portfolio, the results produced by the urn process are superior to those obtained with the Hawkes process and confirm self-excitation.

cond-mat.stat-mech↗

arXiv2021

Pólya urn with memory kernel and asymptotic behaviours of autocorrelation function

Pólya urn is a stochastic process in which balls are randomly drawn from an urn of red and blue balls, and balls of the same color as the drawn balls are added. The probability of a ball of a certain color being drawn is equal to the percentage of balls of that color in the urn. We introduce arbitrary memory kernels to modify this probability. If the memory kernel decays exponentially, it is a stationary process and is mean-reverting. If the memory kernel decays by a power-law, a phase transition occurs and the asymptotic behavior of the autocorrelation function changes. An auxiliary field variable is introduced to transform the process Markovian and the field obeys a multivariate Ornstein-Uhlenbeck process. The exponents of the power law are estimated for the decay of the leading and subleading terms of the autocorrelation function. It is shown that the power law exponents changes discontinuously at the critical point.

cond-mat.stat-mech↗

arXiv2021

Quantum statistics and networks by asymmetric preferential attachment of nodes -- between bosons and fermions

In this article, we discuss the random graph, Barabási-Albert (BA) model, and lattice networks from a unified view point, with the parameter $ω$ with values $1,0,-1$ characterizing these networks, respectively. The parameter is related to the preferential attachment of nodes in the networks and has different weights for the incoming and outgoing links. In addition, we discuss the correspondence between quantum statistics and the networks. Positive and negative $ω$ correspond to Bose and Fermi-like statistics, respectively, and we obtain the distribution that connects the two. When $ω$ is positive, it is related to the threshold of Bose-Einstein condensation (BEC). As $ω$ decreases, the area of the BEC phase is narrowed, and disappears in the limit $ω=0$. When $ω$ is negative, nodes have limits in the number of attachments for newly added nodes (outgoing links), which corresponds to Fermi statistics. We also observe the Fermi degeneracy of the network. When $ω=-1$, a standard Fermion-like network is observed. Fermion networks are realized in the cryptocurrency network "Tangle."

cond-mat.stat-mech↗

arXiv2020

Parameter estimation of default portfolios using the Merton model and Phase transition

We discuss the parameter estimation of the probability of default (PD), the correlation between the obligors, and a phase transition. In our previous work, we studied the problem using the beta-binomial distribution. A non-equilibrium phase transition with an order parameter occurs when the temporal correlation decays by power law. In this article, we adopt the Merton model, which uses an asset correlation as the default correlation, and find that a phase transition occurs when the temporal correlation decays by power law. When the power index is less than one, the PD estimator converges slowly. Thus, it is difficult to estimate PD with limited historical data. Conversely, when the power index is greater than one, the convergence speed is inversely proportional to the number of samples. We investigate the empirical default data history of several rating agencies. The estimated power index is in the slow convergence range when we use long history data. This suggests that PD could have a long memory and that it is difficult to estimate parameters due to slow convergence.

q-fin.RM↗

arXiv2020

Optimal Learning Dynamics of Multi Agents in Restless Multiarmed Bandit Game

Social learning is learning through the observation of or interaction with other individuals; it is critical in the understanding of the collective behaviors of humans in social physics. We study the learning process of agents in a restless multiarmed bandit (rMAB). The binary payoff of each arm changes randomly and agents maximize their payoffs by exploiting an arm with payoff 1, searching the arm at random (individual learning), or copying an arm exploited by other agents (social learning). The system has Pareto and Nash equilibria in the mixed strategy space of social and individual learning. We study several models in which agents maximize their expected payoffs in the strategy space, and demonstrate analytically and numerically that the system converges to the equilibria. We also conducted an experiment and investigated whether human participants adopt the optimal strategy. In this experiment, three participants play the game. If the reward of each group is proportional to the sum of the payoffs, the median of the social learning rate almost coincides with that of the Pareto equilibrium.

physics.soc-ph↗

arXiv2019

Phase transition in the Bayesian estimation of the default portfolio

The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution and consider a multi-year case with a temporal correlation. A phase transition occurs when the temporal correlation decays by power decay. When the power index is less than one, the PD estimator does not converge. It is difficult to estimate the PD with limited historical data. Conversely, when the power index is greater than one, the convergence is the same as that of the binomial distribution. We provide a condition for the estimation of the PD and discuss the universality class of the phase transition. We investigate the empirical default data history of rating agencies and their Fourier transformations to confirm the form of the correlation decay. The power spectrum of the decay history seems to be 1/f, which corresponds to a long memory. But the estimated power index is much greater than one. If we collect adequate historical data,the parameters can be estimated correctly.

q-fin.ST↗

arXiv2019

A voter model on networks and multivariate beta distribution

In elections, the vote shares or turnout rates show a strong spatial correlation. The logarithmic decay with distance suggests that a 2D noisy diffusive equation describes the system. Based on the study of U.S. presidential elections data, it was determined that the fluctuations of vote shares also exhibit a strong and long-range spatial correlation. Previously, it was considered difficult to induce strong and long-range spatial correlation of the vote shares without breaking the empirically observed narrow distribution. We demonstrate that a voter model on networks shows such a behavior. In the model, there are many voters in a node who are affected by the agents in the node and by the agents in the linked nodes. A multivariate Wright-Fisher diffusion equation for the joint probability density of the vote shares is derived. The stationary distribution is a multivariate generalization of the beta distribution. In addition, we also estimate the equilibrium values and the covariance matrix of the vote shares and obtain a correspondence with a multivariate normal distribution. This approach largely simplifies the calibration of the parameters in the modeling of elections.

physics.soc-ph↗