Inverse Limit Shape Problem for Multiplicative Ensembles of Convex Lattice Polygonal Lines

Limit shape of random convex polygonal lines: Even more universality

Limit shape of random convex polygonal lines on Z: Even more universality

The paper is concerned with the limit shape (under some probability measure) of convex polygonal lines on Z+ starting at the origin and with the right endpoint n = (n1, n2) → ∞. In the case of the uniform measure, the explicit limit shape γ∗ was found independently by Vershik, Bárány and Sinai. Bogachev and Zarbaliev recently showed that the limit shape γ∗ is universal in a certain class of mea...

Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts

We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form F(z) = ∞l=1F0(zl) (which entails equal weighting among possible parts l ∈ N). Under mild technical assumptions on the function H0(u) = ln(F0(u)), we show that the limit shape ω∗(x) exists and is given by ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The inverse moment problem for convex polytopes

We present a general and novel approach for the reconstruction of any convex d-dimensional polytope P , assuming knowledge of finitely many of its integral moments. In particular, we show that the vertices of an N-vertex convex polytope in R can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure of degree D), in d + 1 distinct directions in gener...