57 citations · 159 across the 18 of their papers we have counts for
20 papers
Error bounds for composite quantum hypothesis testing and a new characterization of the weighted Kubo-Ando geometric means
Péter E. Frenkel, Milán Mosonyi, Péter Vrana +1
The optimal error exponents of binary composite i.i.d.~state discrimination are trivially bounded by the worst-case pairwise exponents of discriminating individual elements of the…
Integral formula for quantum relative entropy implies data processing inequality
Péter E. Frenkel
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple pr…
On entanglement assistance to a noiseless classical channel
Péter E. Frenkel, Mihály Weiner
For a classical channel, neither the Shannon capacity, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of…
Classical simulations of communication channels
Péter E. Frenkel
We investigate whether certain non-classical communication channels can be simulated by a classical channel with a given number of states and a given `amount' of noise. It is prove…
Estimating the greatest common divisor of the value of two polynomials
Péter E. Frenkel, Gergely Zábrádi
Let be a fixed prime, and let stand for the exponent of in the prime factorization of the integer . Let and be two monic polynomials with integer coeffici…
On the greatest common divisor of the value of two polynomials
Péter E. Frenkel, József Pelikán
We show that if two monic polynomials with integer coefficients have square-free resultant, then all positive divisors of the resultant arise as the greatest common divisor of the…
Convergence of graphs with intermediate density
Péter E. Frenkel
We propose a notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed by László L…
On endomorphisms of the Einstein gyrogroup in arbitrary dimension
Péter E. Frenkel
We determine the automorphisms and the continuous endomorphisms of the Einstein gyrogroup in arbitrary dimension. This generalizes a recent result of Lajos Molnár and Dániel Virosz…
Chromatic roots and limits of dense graphs
Peter Csikvari, Peter E. Frenkel, Jan Hladky +1
In this short note we observe that recent results of Abert and Hubai and of Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic moments of the roots of the…
Polynomial identities for matrices over the Grassmann algebra
Péter E. Frenkel
We determine minimal Cayley--Hamilton and Capelli identities for matrices over a Grassmann algebra of finite rank. For minimal standard identities, we give lower and upper bounds o…
Matchings in Benjamini-Schramm convergent graph sequences
Miklos Abért, Péter Csikvári, Péter Frenkel +1
We introduce the matching measure of a finite graph as the uniform distribution on the roots of the matching polynomial of the graph. We analyze the asymptotic behavior of the matc…
Classical information storage in an -level quantum system
Péter E. Frenkel, Mihály Weiner
A game is played by a team of two --- say Alice and Bob --- in which the value of a random variable is revealed to Alice only, who cannot freely communicate with Bob. Instead,…
Minkowski's inequality and sums of squares
Péter E. Frenkel, Péter Horváth
Positive polynomials arising from Muirhead's inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski's inequality can be rewritten as su…
Benjamini--Schramm continuity of root moments of graph polynomials
Péter Csikvári, Péter E. Frenkel
Recently, M.\ Abért and T.\ Hubai studied the following problem. The chromatic measure of a finite simple graph is defined to be the uniform distribution on its chromatic roots. Ab…
On vector configurations that can be realized in the cone of positive matrices
Péter E. Frenkel, Mihály Weiner
Let ,..., be vectors in an inner product space. Can we find a natural number and positive (semidefinite) complex matrices ,..., of size s…
Remarks on the --permanent
Péter E. Frenkel
We recall Vere-Jones's definition of the --permanent and describe the connection between the (1/2)--permanent and the hafnian. We establish expansion formulae for the --perma…
Pfaffians, hafnians and products of real linear functionals
Péter E. Frenkel
We prove pfaffian and hafnian versions of Lieb's inequalities on determinants and permanents of positive semi-definite matrices. We use the hafnian inequality to improve the lower…
Character formulae for classical groups
P. E. Frenkel
We give formulae relating the value of an irreducible character of a classical group at a matrix to entries of powers of the matrix. This yields a far-reaching generalization of a…
Simple proof of Chebotarev's theorem on roots of unity
P. E. Frenkel
We give a simple proof of Chebotarev's theorem: Let be a prime and a primitive th root of unity. Then all minors of the matrix are non-zero.
On orthogonal invariants in characteristic 2
M. Domokos, P. E. Frenkel
Working over an algebraically closed base field of characteristic 2, the ring of invariants is studied, where is the orthogonal group O(n) or the special orthogonal g…