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  • 1.
    Brändén, Petter
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The Lee-Yang and Pólya-Schur programs. III. Zero-preservers on Bargmann-Fock spaces2014In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 136, no 1, p. 241-253Article in journal (Refereed)
    Abstract [en]

    We characterize linear operators preserving zero-restrictions on entire functions in weighted Bargmann-Fock spaces. This extends the characterization of linear operators on polynomials preserving stability (due to Borcea and the author) to the realm of entire functions, and translates into an optimal, albeit formal, Lee-Yang theorem.

  • 2. Granville, A.
    et al.
    Wigman, Igor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada.
    The distribution of the zeros of random trigonometric polynomials2011In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 133, no 2, p. 295-357Article in journal (Refereed)
    Abstract [en]

    We study the asymptotic distribution of the number Z N of zeros of random trigonometric polynomials of degree N as N →∞. It is known that as N grows to infinity, the expected number of the zeros is asymptotic to N. The asymptotic form of the variance was predicted by Bogomolny, Bohigas and Leboeuf to be cN for some c > 0. We prove that converges to the standard Gaussian. In addition, we find that the analogous result is applicable for the number of zeros in short intervals.

  • 3. Lubotzky, Alexander
    et al.
    Rosenzweig, Lior
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    THE GALOIS GROUP OF RANDOM ELEMENTS OF LINEAR GROUPS2014In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 136, no 5, p. 1347-1383Article in journal (Refereed)
    Abstract [en]

    Let F be a finitely generated field of characteristic zero and Gamma <= GL(n) (F) a finitely generated subgroup. For gamma is an element of Gamma, let Gal(F(gamma)/F) be the Galois group of the splitting field of the characteristic polynomial of gamma over F. We show that the structure of Gal(F(gamma)/F) has a typical behavior depending on F, and on the geometry of the Zariski closure off Gamma (but not on Gamma).

  • 4. Petrosyan, Arshak
    et al.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem2007In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 129, no 6, p. 1659-1688Article in journal (Refereed)
    Abstract [en]

    We consider an obstacle-type problem Delta u = f(x)chi(Omega) in D, u = vertical bar del u vertical bar = 0 on D\Omega, where D is a given open set in R-n and Omega is an unknown open subset of D. The problem originates in potential theory, in connection with harmonic continuation of potentials. The qualitative difference between this problem and the classical obstacle problem is that the solutions here are allowed to change sign. Using geometric and energetic criteria in delicate combination we show the C-1,C-1 regularity of the solutions, and the regularity of the free boundary, below the Lipschitz threshold for the right-hand side.

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