Journal of Statistical Physics最新文献

Recoverable systems provide coarse models of data storage on the two-dimensional square lattice ({mathbb Z}^2). In a recoverable system, each lattice site stores one bit of data, and the overall configuration of bits on the lattice is such that each site can reconstruct the value from its neighbors’ values according to a specified local rule. We initiate a study of such systems through the lens of statistical models for interacting bits on the ({mathbb Z}^2) lattice. We consider two statistical models: (a) an interaction model with a temperature parameter that encourages configurations that respect the local recovery rule, and (b) a hard-core model with an activity parameter, supported only on the admissible configurations of the recoverable system. In this paper, we specifically study the recoverable system in which the admissible configurations are precisely those whose supports form maximal independent sets in the lattice. For the interaction model, we establish uniqueness of the Gibbs measure at high temperature and derive bounds on the entropy in the zero- and low-temperature regimes. For the hard-core model of maximal independent sets, we show phase coexistence at high activity. Unlike the standard hard-core model, however, the maximal version admits nontrivial ground states even at low activity, and we manage to classify them explicitly. We further verify the Peierls condition for appropriately defined contours. Combined with the Pirogov—Sinai theory, this shows that each ground state gives rise to an extremal Gibbs measure, proving phase coexistence at low activity.

We prove that a class of classical lattice models on (mathbb {Z}^d) ((d ge 2)) with on-site space (mathbb {N}_0) and nearest neighbour interaction exhibits long-range checkerboard order at sufficiently high temperature. The ordering mechanism is purely entropic. The class of models contains the recently introduced model of Han et al. [1], by which our work is inspired. The proof uses Pirogov–Sinai theory and the key input is a Peierls bound.

We present a theoretical study of the survival probability of a state initially prepared in the one-particle sector of a multi-qubit system. The motivation for our work is the ongoing laboratory development of multi-qubit platforms based on superconducting circuits. Using elementary concepts of random matrix theory, we obtain analytic expressions for the survival probability in mathematical models of platforms which, albeit stylized, have been previously shown to provide relevant benchmarks for experimental data. In particular, we show that the decay properties are sensitive to the property of the Hamilton operator to have extended states. The survival probability does not appear instead to depend on whether the interaction between qubits is described by a Gaussian orthogonal ensemble (often interpreted as a model of “chaotic” dynamics) or is modeled by an analytically solvable chain. We interpret this phenomenon as a manifestation of a general mechanism for the emergence of equilibration in purely unitary dynamics. Finally, under the same hypothesis of an initial preparation with projection on a large fraction of the extended eigenstates of the Hamilton operator, we show how to extend the classical Kac–Mazur–Montroll estimate of the return time to the quantum survival probability.

We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions—characterized by the location of the uniform distribution and the coupling parameter of the process—where the persistence probabilities have qualitatively different behaviour. We obtain the generating functions of the persistence probabilities explicitly in all possible regions. In some of the regions, the persistence probabilities can be expressed explicitly in terms of various combinatorial quantities.

We prove a simple, explicit lower bound on the radius of a zero-free disk for Gibbs point processes defined by finite-range, repulsive multi-body interactions. Our lower bound improves on those previously known, and we demonstrate that it is essentially sharp in the generality with which our arguments apply. The key ingredient is a multi-body generalization of integral identities for point densities of Gibbs point processes in the spirit of earlier work of Michelen and Perkins.

We propose an extended logistic equation with a generic fluctuating growth rate and solve the resulting random differential equation driven by bounded or unbounded non-white noise, using a previously reported functional method. This approach yields the exact evolution of the probability density function (PDF), moments and dispersion for different types of noise, namely, Gaussian colored noise (GCN), dichotomous noise, decaying noise, and Lévy noise, that may perturb the growth rate of a population. To address the problem of extrema densities for the logistic equation, we obtain exact analytical formulas for the maxima and minima densities, the first-passage time density, and the mean first-passage time for the particular case of Gaussian white noise (GWN). For the GCN, we further introduce an absorbing-boundary approximation that allows us to calculate analytically the maxima, minima, and first-passage time densities. Analytical predictions for the mean first-passage time are validated by Monte Carlo simulations in which the colored-noise trajectories are generated by an exact sampling scheme for the Ornstein-Uhlenbeck process, valid for any discretization step.

Mary Tsingou Menzel was interviewed on November 22, 2024, at her Los Alamos home, with the assistance of her daughter, Ann Menzel.

We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it tries to jump left, the jump is executed. If not, ‘momentum’ is transferred to increase the rate of jumping left of the minimal-label particle. Similarly for jumps to the right. The collision rule is ‘elastic’ in the sense that the net rate of flow of mass is independent of the present configuration, in contrast to the exclusion process, for example. We show that the particle masses and jump rates determine explicitly, via a concave majorant of a simple ‘potential’ function associated to the masses and jump rates, a unique partition of the system into maximal stable subsystems. The internal configuration of each stable subsystem remains tight, while the location of each stable subsystem obeys a strong law of large numbers with an explicit speed. We indicate connections to adjacent models, including diffusions with rank-based coefficients, where, to the authors’ knowledge, the problem of identifying the analogous decomposition into stable sub-systems is yet to be fully solved.

A decoupled standard random walk is a sequence of independent random variables ((hat{S}_n)_{n ge 1}) such that, for each (n ge 1), the distribution of (hat{S}_n) is the same as that of (S_n = xi _1 + ldots + xi _n), where ((xi _k)_{k ge 1}) are independent copies of a nonnegative random variable (xi ). We consider the counting process ((hat{N}(t))_{tge 0}) defined as the number of terms (hat{S}_n) in the sequence ((hat{S}_n)_{n ge 1}) that lie within the interval [0, t]. Under various assumptions on the tail distribution of (xi ), we derive logarithmic asymptotics for the local large deviation probabilities (P{hat{N}(t) = lfloor bE[hat{N}(t)]}) as (t rightarrow infty ) for a fixed constant (b>0). These results are then applied to obtain a logarithmic local large deviations asymptotic for the counting process associated with the infinite Ginibre ensemble and, more generally, for determinantal point processes with the Mittag-Leffler kernel.

This paper considers the parameter estimation for a class of continuous-time stochastic dynamics driven by stochastic differential equations with multiple thresholds, based on discrete-time observations. The underlying state is characterized by state-dependent regime switching, where the drift function changes across different threshold regimes. To address the practically relevant case where both the number and locations of thresholds are unknown, we propose a sequential testing procedure to detect the presence of additional thresholds over a given interval, and develop a method to estimate the locations of thresholds and drift parameters. Building on these results, we propose a SNTD algorithm (sequential algorithm for nonlinear threshold dynamics) to jointly determine the number of thresholds, their locations, and the associated drift parameters. Theoretical guarantees for all proposed estimators are established, including convergence and asymptotic distributions. Simulation studies are provided to demonstrate the effectiveness of the proposed methods.