Related papers: Normal approximation for Gibbs processes via disag…
We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…
We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172--182] for sums of uniformly null…
We prove central limit theorems (CLT) for empirical processes of extreme values cluster functionals as in Drees and Rootz\'en (2010). We use coupling properties enlightened for Dedecker \& Prieur's $\tau-$dependence coefficients in order to…
We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for…
We show that a Gibbs characterization of normalized generalized Gamma processes, recently obtained in Lijoi, Pr\"unster and Walker (2007), can alternatively be derived by exploiting a characterization of exponentially tilted Poisson-Kingman…
We prove that the extremal process of branching Brownian motion, in the limit of large times, converges weakly to a cluster point process. The limiting process is a (randomly shifted) Poisson cluster process, where the positions of the…
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to L{\'e}vy processes in the Skorokhod space…
Foundational Vision-Language models such as CLIP have exhibited impressive generalization in downstream tasks. However, CLIP suffers from a two-level misalignment issue, i.e., task misalignment and data misalignment, when adapting to…
Understanding better the dynamics and steady states of systems strongly coupled to thermal baths is a great theoretical challenge with promising applications in several fields of quantum technologies. Among several strategies to gain access…
We discuss how to perform consistent extractions of anomalous triple gauge couplings (aTGC) from electroweak boson pair production at the LHC in the Standard Model Effective Field Theory (SMEFT). After recasting recent ATLAS and CMS…
Conformal Prediction (CP) algorithms estimate the uncertainty of a prediction model by calibrating its outputs on labeled data. The same calibration scheme usually applies to any model and data without modifications. The obtained prediction…
Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…
Idealized glass transitions are discussed within a novel mode-coupling theory (TMCT) proposed by Tokuyama(Physica A 395,31(2014)). This is done in order to identify common grounds with and differences to the conventional mode-coupling…
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…
The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature $T$. However, non-negligible interactions between system and environment can give rise to an altered state. Here we derive…
We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
Two proofs of the Central Limit Theorem using a renormalization group approach are presented. The first proof is conducted under a third moment assumption and shows that a suitable renormalization group map is a contraction over the space…
We consider characterisations of unitary dilations and approximations of irreversible classical dynamical systems on a Hilbert space. In the commutative case, building on the work in [9], one can express well known approximants (e.g. Hille-…
We show that a modified Empirical process converges to the limiting Gaussian process whenever the limit is continuous. The modification depends on the properties of the limit via Talagrand's characterization of the continuity of Gaussian…