Journal of Statistical Physics最新文献

The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of this distribution, focusing particularly on its moments and asymptotic tail behaviour, in the case where the step distribution is continuous and symmetric, encompassing both diffusive random walks and Lévy flights.

Vladimirov defined an operator on balls in (mathbb {Q}_{p}), the p-adic numbers, analogous to the Laplace operator in the real setting. Kochubei later gave a probabilistic interpretation of this operator. The Vladimirov–Kochubei operator generates a real-time diffusion process in the ring of p-adic integers, a Brownian motion in (mathbb {Z}_{p}). The current work proves that this process is a limit of discrete-time random walks. It motivates the construction of the Vladimirov–Kochubei operator, provides further intuition about ultrametric diffusion, and gives an example of the weak convergence of stochastic processes in a profinite group.

In this paper we consider the two-species Vlasov-Poisson system with a radiation damping term (D^{[3]}(t)) in the whole space (mathbb {R}^3), which was introduced by Bauer [Kinet. Relat. Models 11 (2018), 25–42] to approximate the relativistic Vlasov-Maxwell system, a fundamental model of dynamics of collisionless plasma. We obtain the global existence of solutions and optimal pointwise decay estimates of the charge densities and the electrostatic potential to this system for small initial data without any compact support assumptions. To prove our results, we mainly use the modified vector field method and a bootstrap method. There are two main novelties in our arguments: we introduce new modified functions of modified vector fields to control the troublesome terms involving (D^{[3]}(t)) since it leads to loss an order derivative, and we raise a new bootstrap assumption and carry out new bootstrap arguments.

This paper is concerned with (dge 2) lattice field models with action (V(nabla phi (cdot ))), where (V:mathbb {R}^drightarrow mathbb {R}) is a uniformly convex function. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem.

Identifying key propagation nodes in complex networks is an important research topic. We propose a new gravity model based on weighted multi-feature fusion and approximate influence radius (WMGM) to identify key propagation nodes. The core of this method is to first determine the approximate influence radius of nodes based on node similarity and network structure. Secondly, the normalized maximum eigenvector was introduced, and the element value of the eigenvector was regarded as the node weight value. Then, the K-shell value, degree value, and PageRank centrality of the node are fused, and the fused value is used as the mass of the node. Finally, based on the multi-feature fusion gravity model with weight attribute, the interaction force between nodes was calculated, and the importance score of nodes was determined by accumulating the interaction force of all nodes within the approximate influence radius. The WMGM method is compared with the classical centrality methods, the similar methods, and the state-of-the-art methods on 10 different real datasets. The experimental results show that the WMGM method can effectively identify the top 10 critical nodes in different networks, and the top 200 identified nodes are highly similar to the standard ranking results. In addition, the WMGM achieves high node ranking accuracy across all 10 datasets, attaining the best overall performance on 80% of them.

Ergodic optimization aims to describe properties of invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet with non-unique maximal entropy measures. We show that the space of continuous functions on any Dyck-Motzkin shift contains two disjoint subsets: one is a dense (G_delta ) set with empty interior for which any maximizing measure is not mixing and has zero entropy; the other is a dense set of functions for which there exist uncountably many, fully supported maximizing measures that are Bernoulli. Key ingredients of a proof of this result are the density of closed orbit measures in the space of ergodic measures and the path connectedness of the space of ergodic measures of any Dyck-Motzkin shift.

For a TASEP on (mathbb Z) with the step initial condition we identify limits as (trightarrow infty ) of the expected total number of jumps until time (t>0) and the expected number of active particles at a time t. We also connect the two quantities proving that non-asymptotically, that is as a function of (t>0), the latter is the derivative of the former. Our approach builds on asymptotics derived by Rost and intensive use of the fact that the rightmost particle evolves according to the Poisson process.

We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). The class of geometric-type marginal distributions is preserved by the model with geometric offspring distribution. We give some long-time asymptotic expansions of the parameters of the marginal distribution. From the expansions, we derive the asymptotics of the sustainability probability, marginal distribution, first moment and probability generating function.

In this paper we consider a particular class of solutions of the linear Boltzmann-Rayleigh equation, known in the nonlinear setting as homoenergetic solutions. These solutions describe the dynamics of Boltzmann gases under the effect of different mechanical deformations. Therefore, the long-time behaviour of these solutions cannot be described by Maxwellian distributions and it strongly depends on the homogeneity of the collision kernel of the equation.

Here we focus on the paradigmatic case of simple shear deformations and in the case of cut-off collision kernels with homogeneity (gamma ge 0), in particular covering the case of Maxwell molecules (i.e. (gamma =0)) and hard potentials with (0le gamma <1). We first prove a well-posedness result for this class of solutions in the space of non-negative Radon measures and then we rigorously prove the existence of a stationary solution under the non-equilibrium condition which is induced by the presence of the shear deformation. In the case of Maxwell molecules we prove that there is a different behaviour of the solutions for small and large values of the shear parameter.

We discuss the relaxation time (inverse spectral gap) of the one dimensional O(N) model, for all N and with two types of boundary conditions. We see how its low temperature asymptotic behavior is affected by the topology. The combination of the space dimension, which here is always 1, the boundary condition (free or periodic), and the spin state ({mathbb {S}}^{N-1}), determines the existence or absence of non-trivial homotopy classes in some discrete version. Such non-trivial topology reflects in bottlenecks of the dynamics, creating metastable states that the system exits at exponential times; while when only one homotopy class exists the relaxation time depends polynomially on the temperature. We prove in the one dimensional case that, indeed, the relaxation time is a proxy to the model’s topological properties via the exponential/polynomial dependence on the temperature.