Journal of Statistical Physics最新文献

In the present paper we establish a clear correspondence between probabilities of certain edges belonging to a realization of the uniform spanning tree (UST), and the states of a fermionic Gaussian free field. Namely, we express the probabilities of given edges belonging or not to the UST in terms of fermionic Gaussian expectations. This allows us to explicitly calculate joint probability mass functions of the degree of the UST on a general finite graph, as well as obtain their scaling limits for certain regular lattices.

The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate (varepsilon ) and enstrophy dissipation rates (chi ) for 2D flows sustained by a variety of stochastic driving forces. We show that

in the inviscid limit, consistent with the dual-cascade in 2D turbulence.

This paper addresses large-data local existence and uniqueness of classical solutions to the inhomogeneous Landau equation in the hard potentials case (including Maxwell molecules). Solutions have previously been constructed by Chaturvedi [SIAM J. Math. Anal., 55(5), 5345–5385, 2023] for initial data in an exponentially-weighted (H^{10}) space, but it is not a priori clear whether these solutions have more regularity than the initial data. We improve Chaturvedi’s existence result in two ways: our solutions are (C^infty ) for positive times, and we allow initial data in a sub-exponentially-weighted (L^infty ) space, at the cost of requiring a mild positivity condition at time zero. To prove uniqueness, we require stronger assumptions on the initial data: Hölder continuity and the absence of vacuum regions. These are the same assumptions that are required for uniqueness in prior work on the soft potentials case. Along the way to proving existence and uniqueness, we establish some useful results that were previously only known in the case of soft potentials, including spreading of positivity and propagation of Hölder continuity. Many of the proof strategies from the soft potentials case do not apply here because of the more severe loss of velocity moments.

In recent experiments, ants were constrained to a two-dimensional rectangular domain by enclosing them between two flat transparent surfaces and their dynamic behavior was studied. The large sides of the domain were in the vertical direction and thus, gravity affected the dynamics of the ants. The experiments showed that the collective dynamics of the ants displayed wave-like behavior. In this article, we develop and analyze a mathematical model of the mentioned experiments. Our work contributes to the understanding of the dynamics of active matter and its mathematical modeling.

The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this process relies on Perron-Frobenius theory for adjacency matrices. Generalizing to infinite graphs is rather delicate, and in this article, we study in detail specific models of the MERW on (mathbb {Z}) with loops, for both random and non-random loops. Thanks to an explicit combinatorial representation of the corresponding Perron-Frobenius eigenvectors, we are able to precisely determine the asymptotic behavior of these walks. We show, in particular, that essentially all MERWs on (mathbb {Z}) with loops have positive speed.

The dice lattice is a two-dimensional structure derived from hexagonal and triangular lattices, distinguished by its high degree of symmetry and distinctive physical properties. It holds significant relevance in the fields of mathematics, physics, and materials science, particularly in the investigation of topological phenomena and the dynamic behavior of low-dimensional systems. For a given graph G, let A(G), D(G), and Q(G) represent the adjacency matrix, degree matrix, and signless Laplacian matrix of G, respectively. We define

In this paper, we determine the (A_{alpha })-spectrum and (A_{alpha })-energy of the dice lattice under toroidal boundary conditions. Furthermore, we utilize these findings to derive the A-spectrum, Q-spectrum, A-energy, and Q-energy of the dice lattice with the same boundary conditions.

Consensus behavior is a notable emergence phenomenon in nature. It is only recently that consensus behavior has been demonstrated in the Vlasov alignment and Euler alignment models with low-order power-law potentials, i.e. (U(r)=r^{alpha }, alpha in [1,4)). Note that the attraction between particles weakens as (alpha ) grows, so it is interesting to consider the high-order power-law potential case. By some macroscopic and microscopic Lyapunov functionals, for any (alpha in (2,infty )) and any long range communication weight, we establish both the weak and strong consensus and their precise convergence rates for the Vlasov alignment and Euler alignment models.

We introduce a periodic extension of the Kingman model [11] for the balance between selection and mutation in large populations. In its original form, the model describes a population’s fitness distribution by a probability measure on the unit interval evolving through a simple discrete-time dynamical system, in which selection operates via size-biasing, and the mutation distribution remains constant along time. We allow the mutation environment to vary periodically over time and prove the convergence of the fitness distribution along subsequences; crucially, we derive an explicit criterion, phrased in term of the Perron eigenvalue of a characteristic matrix, to determine whether an atom emerges at the largest fitness in the limit, a phenomenon called condensation. Our results provide new insights on the role of periodic mutation effects in population Darwinian evolution.

Quantum systems in thermal equilibrium are described using Gibbs states. The correlations in such states determine how difficult it is to describe or simulate them. In this article, we show that if the Gibbs state of a quantum system satisfies that each of its marginals admits a local effective Hamiltonian with short-range interactions, then it satisfies a mixing condition, that is, for any regions A, C the distance of the reduced state (rho _{AC}) on these regions to the product of its marginals, ( left| rho _{AC} rho _A^{-1} otimes rho _C^{-1} - mathbbm {1}_{AC} right| , , ) decays exponentially with the distance between regions A and C. This mixing condition is stronger than other commonly studied measures of correlation. In particular, it implies the exponential decay of the mutual information between distant regions. The mixing condition has been used, for example, to prove positive log-Sobolev constants. On the way, we prove that the the condition regarding local effective Hamiltonian is satisfied if the Hamiltonian only has commuting interactions which also commute with every marginal of their products. The proof of these results employs a variety of tools such as Araki’s expansionals, quantum belief propagation and cluster expansions.