Journal of Statistical Physics最新文献

For the elephant random walk, namely, the elephant random walk with deterministic step sizes, rates of moment convergence have been obtained by Hayashi, Oshiro and Takei [J. Stat. Mech. Theory Exp., 2023]. In this paper, we extend above results to the elephant random walk with random step sizes, namely, we obtained rates of moment convergence for the position of the walker when memory parameter (alpha in (-1, 1)).

Spectral form factor (SFF), one of the key quantity from random matrix theory, serves as an important tool to probe universality in disordered quantum systems and quantum chaos. In this work, we present exact closed-form expressions for the second- and third-order SFFs in the circular unitary ensemble (CUE), valid for all real values of the time parameter, and analyze their asymptotic behavior in different regimes. In particular, for the second-order SFF, we derive an exact closed-form expression in terms of polygamma functions. In the limit of infinite matrix size, and when the time parameter is restricted to integer values, the second-order SFF reproduces the standard result established in earlier studies. When the time parameter is of order one relative to the matrix size, we demonstrate that the second-order SFF grows logarithmically with the ensemble dimension. For the third-order SFFs, a closed-form result in a special case is obtained by exploiting the translational invariance of CUE.

In this paper, we study fluctuations and moderate deviations for a discrete energy Kac-like walk associated with a Boltzmann-type equation. We show that the fluctuations of the empirical measure around the Boltzmann-type equation converge in law to an infinite dimensional Ornstein-Uhlenbeck process, and establish the moderate deviation principle for the empirical measure.

This work investigates the stochastic dynamics of Hamiltonian systems with hyperbolic structure under external noise. To overcome the conflict between the non-anticipative nature of stochastic solutions and the exponential dichotomies of the hyperbolic structure, we construct auxiliary processes that are distributionally equivalent to the original dynamics. This construction allows us to leverage both explicit stable/unstable splittings (when available) and the Oseledets decomposition provided by the Multiplicative Ergodic Theorem (in the fully stochastic case). Within this framework, we prove central limit theorems and functional central limit theorems for the time-integrated normal deviations, with limiting covariances given explicitly in terms of the system parameters. These results establish the distributional characterization of hyperbolic tori persistence under stochastic perturbations, illustrating how tools from stochastic analysis and ergodic theory yield precise answers to a classical problem in Hamiltonian dynamics.

Consider the convex hull of a collection of disjoint open discs with radii 1/2. The boundary of the convex hull consists of a finite number of line segments and arcs. Randomly choose a point in one of the arcs in the boundary so that the density of its distribution is proportional to the total arc measure. Attach a new disc at the chosen point so that it is outside of the convex hull and tangential to its boundary. Replace the original convex hull with the convex hull of all preexisting discs and the new disc. Continue in the same manner. Simulations show that disc clusters form long, straight, or slightly curved filaments with many small side branches and occasional macroscopic side branches. For a large number of discs, the shape of the convex hull is either an equilateral triangle or a quadrangle. Side branches play the role analogous to avalanches in sandpile models, one of the best-known examples of self-organized criticality (SOC). Our simulation and theoretical results indicate that the size of a branch obeys a power law, as expected of avalanches in sandpile models and similar “catastrophies” in other SOC models.

In this paper, we study the oriented swap process on the positive integers and its asymptotic properties. Our results extend a theorem by Angel, Holroyd, and Romik regarding the trajectories of particles in the finite oriented swap process. Furthermore, we study the evolution of the type of a particle at the leftmost position over time. Our approach relies on a relationship between multi-species particle systems and Hecke algebras, complemented by a detailed asymptotic analysis.

In this paper, we study the homogeneous multi-component Curie-Weiss-Potts model with (q ge 3) spins. The model is defined on the complete graph (K_{Nm}), whose vertex set is equally partitioned into m components of size N. For a configuration (sigma : {1, cdots , Nm} rightarrow {1, cdots , q},) the Gibbs measure is defined by

where (Z_{N, beta }) is the normalizing constant, and (beta >0) is the inverse-temperature parameter. The interaction coefficient is

where (J in (0, 1)) is the relative strength of inter-component interaction to intra-component interaction. We identify a dynamical phase transition at the critical inverse-temperature (beta _{s}(q)), which is the same threshold as for the one-component Potts model [5] and depends only on the number of spins q,  but is independent of the number of components m and relative interaction strength (J in (0, 1).) By extending the aggregate path method [19] to multi-component setting, we prove that the mixing time is (O(N log N)) in the subcritical regime (beta <beta _{s}(q).) In the supercritical regime (beta > beta _{s}(q),) we further show that the mixing time is exponential in N via a metastability analysis. This is the first result for the dynamical phase transition in the multi-component Potts model.

Quantum cross entropy is a measure of information that quantifies the difference between two quantum states. In this paper, we first define the local quantum cross entropy based on local quantum Bernoulli noises (LQBNs) and examine several of its relevant properties, including its relationships with local quantum entropy and local quantum relative entropy, as well as its non-negativity, asymmetry, monotonicity, and unitary invariance with respect to the second parameter. Then, we investigate the local quantum cross entropy between any local quantum state and the normalized identity operator. Finally, we research its application in local quantum data compression.

Two new interacting particle systems are introduced in this paper: dynamic versions of the asymmetric inclusion process (ASIP) and the asymmetric Brownian energy process (ABEP). Dualities and reversibility of these processes are proven, where the quantum algebra ({mathcal {U}}_q(mathfrak {su}(1,1))) and the Al-Salam–Chihara polynomials play a crucial role. Two hierarchies of duality functions are found, where the Askey-Wilson polynomials and Jacobi polynomials sit on top.

An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie–Weiss–type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral representation of the grand partition function, we apply Laplace’s method to obtain asymptotically exact expressions for the pressure, density and equation of state. The phase diagram of the model exhibits a hierarchy of first-order phase transition lines, each terminating at a critical point. We determine the coordinates of the first five such points. Recasting the formalism in dimensionless variables highlights the explicit temperature dependence of all thermodynamic functions. This enables us to derive a closed-form expression for the entropy. The results reveal pronounced entropy minima around integer cell occupancies and reproduce density-anomaly isotherm crossings analogous to those in core-softened models.