Related papers: Local Laws and a Mesoscopic CLT for $\beta$-ensemb…
We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied…
The nature of the electron gas is characterized, above all, by its multi-particle correlations. The conserving sum rules for the electron gas have been thoroughly studied for many years, and their centrality to the physics of metallic…
In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied,…
Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature d.c. resistivity, requires a significant low energy spectral weight at finite momentum. One way to achieve this is via a Fermi surface…
We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
In this paper we introduce a method of calculating the local temperature and chemical potential inside a mesoscopic device out of equilibrium. We show how to check the conditions of local thermal equilibrium as the whole system is out of…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
We develop a new systematic procedure for the Regge limit in perturbative QCD to arbitrary logarithmic order. The formalism relies on the IR structure and the gauge symmetry of the theory. We identify leading regions in loop momentum space…
Recent photoemission experiments \cite{dessau} reveal that the excitations along the nodal region in the strange metal of the cuprates, rather than corresponding to poles in the single-particle Green function, exhibit power-law scaling as a…
We investigate the thermodynamic efficiency of sub-micro-scale heat engines operating under the conditions described by over-damped stochastic thermodynamics. We prove that at maximum power the efficiency obeys for constant isotropic…
We reanalyse the work of Cleuren et al., Phys. Rev. Lett. 109, 248902 (2012), in the light of Jiang et al. Phys. Rev. B 85, 075412 (2012). The condition for cooling enforces its rate to be exponentially small at low temperatures. Thus, the…
Events in mesoscopic systems often take place at first-passage times, as is for instance the case for a colloidal particle that escapes a metastable state. An interesting question is how much work an external agent has done on a particle…
Studies of mesoscopic structures have now become a leading and rapidly evolving research field ranging from physics, chemistry, and mineralogy to life sciences. The increasing miniaturization of devices with length scales of a few…
We find universal structure and scaling of BEC statistics and thermodynamics for mesoscopic canonical-ensemble ideal gas in a trap for any parameters, including critical region. We identify universal constraint-cut-off mechanism that makes…
In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity \(\beta_\sigma(f_0')\) which encapsulates local monotonicity and…
We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to solve a long-standing problem of identifying the underlying cause of the second law (SL) of spontaneous irreversibility, a stochastic universal principle, as the mechanical…
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy \[H_n=\sum_{1\le j<k\le n}\omega_j\omega_k1_{\{S_j=S_k\}}\] of the polymer $\{S_1,...,S_n\}$ equipped with random…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
We study the individual digits for the absolute value of the characteristic polynomial for the Circular $\beta$-Ensemble. We show that, in the large $N$ limit, the first digits obey Benford's Law and the further digits become uniformly…
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…