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Under mild structural assumptions and regularity conditions on the marginal and conditional densities, an explicit bound on the $β$-mixing coefficients in terms of the physical dependence measure is provided. Consequently, weak physical dependence implies $β$-mixing and strong mixing for triangular arrays, complementing Hill (2025), who proved the converse implication under moment assumptions.

The untraceability of transactions facilitated by Ethereum mixing services like Tornado Cash poses significant challenges to blockchain security and financial regulation. Existing methods for correlating mixing accounts suffer from limited labeled data and vulnerability to noisy annotations, which restrict their practical applicability. In this paper, we propose StealthLink, a novel framework that addresses these limitations through cross-task domain-invariant feature learning. Our key innovation lies in transferring knowledge from the well-studied domain of blockchain anomaly detection to the data-scarce task of mixing transaction tracing. Specifically, we design a MixFusion module that constructs and encodes mixing subgraphs to capture local transactional patterns, while introducing a knowledge transfer mechanism that aligns discriminative features across domains through adversarial discrepancy minimization. This dual approach enables robust feature learning under label scarcity and distribution shifts. Extensive experiments on real-world mixing transaction datasets demonstrate that StealthLink achieves state-of-the-art performance, with 96.98\% F1-score in 10-shot learning scena

Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Further, we adapt the techniques from separable qudits to the fermionic setting and prove rapid mixing of the strongly-interacting regime of the Fermi-Hubbard model, for which we also explicitly evaluate the guaranteed parameter regimes. Our results constitute the first efficient mixing bounds for non-commuting qudit mode

We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagnetic Curie-Weiss model, the anti-ferromagnetic Ising model on expander graphs, and the Sherrington-Kirkpatrick model with disorder of negative mean. Existing approaches to rapid mixing rely crucially on log-concavity or spectral width bounds and therefore can break down in the presence of a negative outlier. To address this difficulty, we develop a new covariance approximation method based on Gaussian approximation. This method is implemented via an iterative application of Stein's method to quadratic tilts of sums of bounded random variables, which may be of independent interest. The resulting analysis provides an operator-norm control of the full correlation structure under arbitrary external fields. Combined with the localization schemes of Eldan and Chen, these estimates lead to a modified logarithmic Sobolev inequality and near-optimal mixing time bounds in regimes where spectral width bounds fail. We complement these results by proving exponential lower bounds on the mixing time for low temperature ant

In this paper, we show that Gibbs measures on self-conformal sets generated by a $C^{1+α}$ conformal IFS on $\mathbb{R}^d$ satisfying the OSC are exponentially mixing. We exploit this to obtain essentially sharp asymptotic counting statements for the recurrent and the shrinking target subsets associated with any such set. In particular, we provide explicit examples of dynamical systems for which the recurrent sets exhibit (unexpected) behavior that is not present in the shrinking target setup. In the process of establishing our exponential mixing result we extend Mattila's rigidity theorem for self-similar sets to self-conformal sets without any separation condition and for arbitrary Gibbs measures.

We study the mixing time of the single-site update Markov chain, known as the Glauber dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal convergence results for arbitrary trees. We consider the more general problem of sampling from the Gibbs distribution in the hard-core model where independent sets are weighted by a parameter $λ>0$; the special case $λ=1$ corresponds to the uniform distribution over all independent sets. Previous work of Martinelli, Sinclair and Weitz (2004) obtained optimal mixing time bounds for the complete $Δ$-regular tree for all $λ$. However, Restrepo et al. (2014) showed that for sufficiently large $λ$ there are bounded-degree trees where optimal mixing does not hold. Recent work of Eppstein and Frishberg (2022) proved a polynomial mixing time bound for the Glauber dynamics for arbitrary trees, and more generally for graphs of bounded tree-width. We establish an optimal bound on the relaxation time (i.e., inverse spectral gap) of $O(n)$ for the Glauber dynamics for unweighted independent sets on arbitrary trees. We stress that our results hold for arbitrary trees and there is no dependence on the maximum degree $Δ

We prove that the mixing time of the No-U-Turn Sampler (NUTS), when initialized in the concentration region of the canonical Gaussian measure, scales as $d^{1/4}$, up to logarithmic factors, where $d$ is the dimension. This scaling is expected to be sharp. This result is based on a coupling argument that leverages the geometric structure of the target distribution. Specifically, concentration of measure results in a striking uniformity in NUTS' locally adapted transitions, which holds with high probability. This uniformity is formalized by interpreting NUTS as an accept/reject Markov chain, where the mixing properties for the more uniform accept chain are analytically tractable. Additionally, our analysis uncovers a previously unnoticed issue with the path length adaptation procedure of NUTS, specifically related to looping behavior, which we address in detail.

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $μ$, random walks with respect to $μ$ will produce elements with strong mixing properties for this action asymptotically almost surely. In particular, when the group has no finite normal subgroups this implies that the action is highly topologically transitive. Along the way, we prove technical results about convex cocompact subgroups which allow us to extend some results on random walks of Abbott and the first author.

We investigate the mixing coefficients of interval maps satisfying Rychlik's conditions. A mixing Lasota-Yorke map is reverse $φ$-mixing. If its invariant density is uniformly bounded away from 0, it is $φ$-mixing iff all images of all orders are big in which case it is $ψ$-mixing. Among $\b$-transformations, non-$φ$-mixing is generic. In this sense, the asymmetry of $φ$-mixing is natural.

$Z^\prime$ models belong to the ones that can most easily explain the anomalies in $b\to s μ^+μ^-$ transitions. However, such an explanation by a single $Z^\prime$ gauge boson, as done in the literature, is severly constrained by the $B^0_s-\bar B_s^0$ mixing. Also the recent finding, hat the mass differences $ΔM_s$, $ΔM_d$, the CP-violating parameter $\varepsilon_K$, and the mixing induced CP-asymmetries $S_{ψK_S}$ and $S_{ψφ}$ can be simultaneously well described within the SM without new physics (NP) contributions, is a challenge for $Z^\prime$ models with a single $Z^\prime$ contributing at tree-level to quark mixing. We point out that including a second $Z^\prime$ in the model allows to eliminate simultaneously tree-level contributions to the five $ΔF=2$ observables used in the determination of the CKM parameters while leaving the room for NP in $ΔM_K$ and $ΔM_D$. The latter one can be removed at the price of infecting $ΔM_s$ or $ΔM_d$ by NP which is presently disfavoured. This pattern is transparently seen using the new mixing matrix for $Z^\prime$ interactions with quarks. This strategy allows significant tree-level contributions to $K$, $B_s$ and $B_d$ decays thereby allowi

Various extensions of the Standard Model predict the existence of hidden photons kinetically mixing with the ordinary photon. This mixing leads to oscillations between photons and hidden photons, analogous to the observed oscillations between different neutrino flavors. In this context, we derive new bounds on the photon-hidden photon mixing parameters using the high precision cosmic microwave background spectral data collected by the Far Infrared Absolute Spectrophotometer instrument on board of the Cosmic Background Explorer. Requiring the distortions of the CMB induced by the photon-hidden photon mixing to be smaller than experimental upper limits, this leads to a bound on the mixing angle < 10^{-7}-10^{-5} for hidden photon masses between 10^{-14} eV and 10^{-7} eV. This low-mass and low-mixing region of the hidden photon parameter space was previously unconstrained.

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds nu

Enhancing and controlling chaotic advection or chaotic mixing within liquid droplets is crucial for a variety of applications including digital microfluidic devices which use microscopic ``discrete'' fluid volumes (droplets) as microreactors. In this work, we consider the Stokes flow of a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we have shown in previous work that the rotation not only leads to one or more three-dimensional chaotic mixing regions, in which mixing occurs through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of chaotic mixing within the drop. Such a control was achieved through appropriate tuning of the amplitude and frequency of the rotation in order to use resonances between the natural frequencies of the system and those of the external forcing. In this paper, we study the influence of the orientation of the rotation axis on the chaotic mixing zones as a third parameter, as well as propose an experimental set up to implement the techniques discussed.

The bounds on the neutrino mixing angles and CP Dirac phase for an SO(10) model with lopsided mass matrices, arising from the presence of ${\bf 16}_H$ and $\bar{\bf 16}_H$ Higgs representations, are studied by variation of the one real and three unknown complex input parameters for the right-handed Majorana neutrino mass matrix. The scatter plots obtained favor nearly maximal atmospheric neutrino mixing, while the reactor neutrino mixing lies in the range $10^{-5} \lsim \sin^2 θ_{13} \lsim 1 \times 10^{-2}$ with values greater than $10^{-3}$ most densely populated. A rather compelling scenario within the model follows, if we restrict the three unknown complex parameters to their imaginary axes and set two of them equal. We then find the scatter plots are reduced to narrow bands, as the mixing angles and CP phase become highly correlated and predictive. The bounds on the mixing angles and phase then become $0.45 \lsim \sin^2 θ_{23} \lsim 0.55$, $0.38 \lsim \tan^2 θ_{12} \lsim 0.50$, $0.002 \lsim \sin^2 θ_{13} \lsim 0.003$, and $60^\circ \lsim \pm δ_{CP} \lsim 85^\circ$. Moreover, successful leptogenesis and subsequent baryogenesis are also obtained, with $η_B$ increasing from $(2.7

We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in the Sobolev space $W^{s,p}$, where $s \geq 0$ and $1\leq p\leq \infty$. The mixing properties are given in terms of a characteristic length scale, called the mixing scale. We consider two notions of mixing scale, one functional, expressed in terms of the homogeneous Sobolev norm $\dot H^{-1}$, the other geometric, related to rearrangements of sets. We study rates of decay in time of both scales under self-similar mixing. For the case $s=1$ and $1 \leq p \leq \infty$ (including the case of Lipschitz continuous velocities, and the case of physical interest of enstrophy-constrained flows), we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound, established in previous works, on the time decay of both scales. We also present several consequences for the geometry of regular Lagrangian flows associated to Sobolev velocity fields.

Development of the Richtmyer-Meshkov instability leads to mixing of two substances separated by contact boundary. Mixture of two fluids is confined between two mixing fronts. Universal asymptotics follows the transition stage at late time. Functions which describe the fronts penetration asymptoticaly transform to power law dependences. Mixing is acompanied by cascade of enlarging of dominant scale of a turbulent mixing zone. The exponents of the power laws are: 2/5 for 2D and 1/3 for 3D cases. These exact exponents are calculated in our work. They are determined by the mechanism of redistribution of momentum from small into the large scales.

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt density}" ratio convergence for every pair of measurable sets in a dense hereditary ring. Rational weak mixing implies weak rational ergodicity and (spectral) weak mixing. It is enjoyed for example by Markov shifts with Orey's strong ratio limit property. The power, subsequence version of the property is generic.

In the type-I seesaw model the size of mixing between light and heavy neutrinos, nu and N, respectively, is of order the square root of their mass ratio, (m_nu/m_N)^(1/2), with only one generation of the neutrinos. Since the light-neutrino mass must be less than an eV or so, the mixing would be very small, even for a heavy-neutrino mass of order a few hundred GeV. This would make it unlikely to test the model directly at the LHC, as the amplitude for producing the heavy neutrino is proportional to the mixing size. However, it has been realized for some time that, with more than one generation of light and heavy neutrinos, the mixing can be significantly larger in certain situations. In this paper we explore this possibility further and consider specific examples in detail in the context of type-I seesaw. We study its implications for the single production of the heavy neutrinos at the LHC via the main channel q qbar' -> W^* -> l N involving an ordinary charged lepton l. We then extend the discussion to the type-III seesaw model, which has richer phenomenology due to presence of the charged partners of the heavy neutrinos, and examine the implications for the single production

We have developed a quantum field theoretic framework for scalar and pseudoscalar meson mixing and oscillations in time. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is proven and shown to lead to a rich condensate structure. This is exploited to develop formulas for two flavor boson oscillations in systems of arbitrary boson occupation number. The mixing and oscillation can be understood in terms of vacuum condensate which interacts with the bare particles to induce non-trivial effects. We apply these formulas to analyze the mixing of $η$ with $η'$ and comment on the $K_L K_S$ system. In addition, we consider the mixing of boson coherent states, which may have future applications in the construction of meson lasers.