Journal of Statistical Physics最新文献

According to the Bogoliubov theory the low energy behaviour of the Bose gas at zero temperature can be described by non-interacting bosonic quasiparticles called phonons. In this work the damping rate of phonons at low momenta, the so-called Beliaev damping, is explained and computed with simple arguments involving the Fermi Golden Rule and Bogoliubov’s quasiparticles.

This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein–Kantorovich–Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration is driven either by a Brownian motion, a symmetric (alpha )-stable Lévy process, a stationary Gaussian or (alpha )-stable Ornstein–Uhlenbeck process, or by a general Lévy process with second moments. The obtained non-asymptotic bounds establish asymptotically abrupt thermalization. The analysis is based on the explicit representation of the solution of the system in terms of convolutions of Bessel functions.

The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on (mathbb {R}^n) that are constrained to a scaled ((n-1))-dimensional (ell _1)-sphere, equivalently a scaled ((n-1))-dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables.

The behavior of (b=2) real-space renormalization group (RSRG) maps like the majority rule and the decimation map was examined by numerically applying RSRG steps to critical (q=2,3,4) Potts spin configurations. While the majority rule is generally believed to work well, a more thorough investigation of the action of the map has yet to be considered in the literature. When fixing the size of the renormalized lattice (L_g) and allowing the source configuration size (L_0) to vary, we observed that the RG flow of the spin and energy correlation under the majority rule map appear to converge to a nontrivial model-dependent curve. We denote this property as “faithfulness”, because it implies that some information remains preserved by RSRG maps that fall under this class. Furthermore, we show that (b=2) weighted majority-like RSRG maps acting on the (q=2) Potts model can be divided into two categories, maps that behave like decimation and maps that behave like the majority rule.

In order to obtain functional limit theorems for heavy-tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by means of a structure called the pilling process introduced recently in the context of dynamical systems. So far, the pilling process has been computed only for observable functions maximised at a single repelling fixed point. Here, we study richer clustering behaviours by considering correlated maximal sets, in the sense that the observable is maximised in multiple points belonging to the same orbit, and we work out explicit expressions for the pilling process when the dynamics is piecewise linear and expanding (1-dimensional and 2-dimensional).

We study a geometric version of first-passage percolation on the complete graph, known as long-range first-passage percolation. Here, the vertices of the complete graph (mathcal {K}_n) are embedded in the d-dimensional torus (mathbb T_n^d), and each edge e is assigned an independent transmission time (T_e=Vert eVert _{mathbb T_n^d}^alpha E_e), where (E_e) is a rate-one exponential random variable associated with the edge e, (Vert cdot Vert _{mathbb T_n^d}) denotes the torus-norm, and (alpha ge 0) is a parameter. We are interested in the case (alpha in [0,d)), which corresponds to the instantaneous percolation regime for long-range first-passage percolation on (mathbb {Z}^d) studied by Chatterjee and Dey [14], and which extends first-passage percolation on the complete graph (the (alpha =0) case) studied by Janson [24]. We consider the typical distance, flooding time, and diameter of the model. Our results show a 1, 2, 3-type result, akin to first-passage percolation on the complete graph as shown by Janson. The results also provide a quantitative perspective to the qualitative results observed by Chatterjee and Dey on (mathbb {Z}^d).

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the periodic probabilities of states connected by these observed transitions and their time-dependent transition rates can be inferred. Moreover, the smallest number of hidden transitions between accessible ones and some of their transition rates can be extracted. We prove and conjecture lower bounds on the total entropy production for such periodic stationary states. Even though our techniques are based on generalizations of known methods for steady states, we obtain original results for those as well.

We determine diameters of Markov chains describing one-dimensional N-particle models with an exclusion interaction, namely the symmetric simple exclusion process (Ssep) and one of its non-reversible liftings, the lifted totally asymmetric simple exclusion process (Tasep). The diameters provide lower bounds for the mixing times, and we discuss the implications of our findings for the analysis of these models.

We prove the existence and uniqueness of multiple (hbox {SLE}_{kappa }) associated with any given link pattern for (kappa in (4,6]). We also have the uniqueness for (kappa in (6,8)). The multiple (hbox {SLE}_{kappa }) law is constructed by first inductively constructing a (sigma )-finite multiple (hbox {SLE}_{kappa }) measure and then normalizing the measure whenever it is finite. The total mass of the measure satisfies the conformal covariance, asymptotics and PDE for multiple (hbox {SLE}_{kappa }) partition functions in the literature subject to the assumption that it is smooth.