相关论文: Large deviations analysis for random combinatorial…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation…
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single…
In this study, we consider unsupervised clustering of categorical vectors that can be of different size using mixture. We use likelihood maximization to estimate the parameters of the underlying mixture model and a penalization technique to…
The modeling of bio-molecular system across molecular scales remains a central challenge in scientific research. Large language models (LLMs) are increasingly applied to bio-molecular discovery, yet systematic evaluation across multi-scale…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…
We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional…
The effect of bulk dissipation on non critical sandpile models is studied using both multifractal and finite size scaling analyses. We show numerically that the local limited (LL) model exhibits a crossover from multifractal to self-similar…
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large…
Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…
We employ perturbative RG and $\epsilon$-expansion to study multi-critical single-scalar field theories with higher derivative kinetic terms of the form $\phi(-\Box)^k\phi$. We focus on those with a $\mathbb{Z}_2$-symmetric critical point…
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects…
A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the…
This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based…
The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established…
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…
The field mixing that manifests broken particle-hole symmetry is studied for a 2-D asymmetric lattice gas model having tunable field mixing properties. Monte Carlo simulations within the grand canonical ensemble are used to obtain the…