Related papers: Multiplicative characters and Gaussian fluctuation…
We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of…
We obtain a new bound on certain double sums of multiplicative characters improving the range of several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical…
One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity…
A classical result of Paley shows that there are infinitely many quadratic characters $\chi\mod{q}$ whose character sums get as large as $\sqrt{q}\log \log q$; this implies that a conditional upper bound of Montgomery and Vaughan cannot be…
Quantum fluctuation expression of the baryon number for a subsystem consisting of hot relativistic spin-$\frac{1}{2}$ particles are derived. These fluctuations seems to diverge in the limit where system size goes to zero. For a broad range…
Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let $\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP} gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and the number of…
Quantum fluctuations impose fundamental limits on measurement and space-time probing. Although using optimised probe fields can allow to push sensitivity in a position measurement beyond the "standard quantum limit", quantum fluctuations of…
Let $G$ be a finite reductive group defined over a finite field $F_q$. In the case where $G$ is a special linear group, we compute the multiplicities of irreducible characters of $G(F_{q^2})$ with the character of $G(F_{q^2})$ induced from…
The principal results of this contribution are the weak and strong limits of maxima of contracted stationary Gaussian random sequences. Due to the random contraction we introduce a modified Berman condition which is sufficient for the weak…
We introduce the two user finite state compound Gaussian interference channel and characterize its capacity region to within one bit. The main contributions involve both novel inner and outer bounds. The inner bound is multilevel…
We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova…
We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in…
Some nondifferentiable quantities (for example, the metric signature) can be the independent physical degrees of freedom. It is supposed that in quantum gravity these degrees of freedom can fluctuate. Two examples of such quantum…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
Gelfand-Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the…
Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate…
In this paper, we present explicit description on the additive characters, multiplicative characters and Gauss sums over a local ring. As an application, based on the additive characters and multiplicative characters satisfying certain…
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.
The Macroscopic Fluctuation Theory is an effective framework to describe transports and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the Macroscopic Fluctuation Theory may be extended to the quantum realm…