Related papers: Upper Bounds for Mutations of Potentials

A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,\delta)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $\delta$. Previous works introduced this concept and study when…

Let $L/K$ be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of ${\rm Gal}(L/K)$, the sharper of which is conditional on the Artin Conjecture and the…

Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of…

This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altu\u{g} and Wagner is given, and the result is…

Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy-momentum relations of those electrons. They can thus be used to place bounds on…

This work studies the generalized Moran process, as introduced by Lieberman et al. [Nature, 433:312-316, 2005]. We introduce the parameterized notions of selective amplifiers and selective suppressors of evolution, i.e. of networks (graphs)…

In this paper, new relations between the derivatives of the Legendre polynomials are obtained, and by these relations, new upper bounds for the Legendre coefficients of differentiable functions are presented. These upper bounds are sharp…

We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z),…

The completeness of quantum mechanics in predictive power is a central question in its foundational study. While most investigations focus on two-dimensional systems, high-dimensional systems are more general and widely applicable. Building…

An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers.…

In this paper, parameterized Gallager's first bounding technique (GFBT) is presented by introducing nested Gallager regions, to derive upper bounds on the ML decoding error probability of general codes over AWGN channels. The three…

We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fields to give an explicit upper bound on trilinear…

The study of Fourier transforms of probability measures on fractal sets plays an important role in recent research. Faster decay rates are known to yield enhanced results in areas such as metric number theory. This paper focuses on…

Quantum lattice models describe a wide array of physical systems, and are a canonical way to numerically solve the Schrodinger equation. Here we prove the potential inversion theorem, which says that wavefunction probability in these models…

Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…

For each $n$, let $\text{RD}(n)$ denote the minimum $d$ for which there exists a formula for the general polynomial of degree $n$ in algebraic functions of at most $d$ variables. In 1945, Segre called for a better understanding of the large…

We present an improved version of Diaconis' upper bound lemma, which is used to compute the limiting value of the distance to stationarity. We then apply it to random transpositions studied by Diaconis and Shahshahani.

We consider two eliiptic overdetermined boundary value problems. There are variants on J. Serrin's 1971 classical results and having the same conclusion that the domains should be forcibly Euclidean balls.

We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.

In this paper, we introduce and study the quantum deformations of the cluster superalgebra. Then we prove the quantum version of the Laurent phenomenon for the super-case.