Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Parzanchevski, Ori"'
Autor:
Evra, Shai, Parzanchevski, Ori
The Clifford+T gate set is a topological generating set for PU(2), which has been well-studied from the perspective of quantum computation on a single qubit. The discovery that it generates a full S-arithmetic subgroup of PU(2) has led to a fruitful
Externí odkaz:
http://arxiv.org/abs/2401.16120
In their seminal paper, Lubotzky, Phillips and Sarnak (LPS) defined the notion of regular Ramanujan graphs and gave an explicit construction of infinite families of $(p+1)$-regular Ramanujan Cayley graphs, for infinitely many $p$. In this paper we ex
Externí odkaz:
http://arxiv.org/abs/2312.06507
Autor:
Alev, Vedat Levi, Parzanchevski, Ori
It is well known that the spectral gap of the down-up walk over an $n$-partite simplicial complex (also known as Glauber dynamics) cannot be better than $O(1/n)$ due to natural obstructions such as coboundaries. We study an alternative random walk ov
Externí odkaz:
http://arxiv.org/abs/2312.02089
Autor:
Kaufman, Tali, Parzanchevski, Ori
Publikováno v:
International Mathematics Research Notices, 2022:19, October 2022, Pages 14741-14769
Powering the adjacency matrix of an expander graph results in a better expander of higher degree. In this paper we seek an analogue operation for high-dimensional expanders. We show that the naive approach to powering does not preserve high-dimension
Externí odkaz:
http://arxiv.org/abs/1909.02473
Publikováno v:
Philosophical Transactions of the Royal Society A, 378 (2020), no. 2163
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments are surveyed
Externí odkaz:
http://arxiv.org/abs/1904.03533
Autor:
Chapman, Michael, Parzanchevski, Ori
Publikováno v:
Commentarii Mathematici Helvetici, 97(3):431-456, 2022
The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and cutoff on sparse graphs in general. In this paper we establis
Externí odkaz:
http://arxiv.org/abs/1901.09383
Autor:
Evra, Shai, Parzanchevski, Ori
Publikováno v:
Geometric and Functional Analysis 32:193-235 (2022)
In a seminal series of papers from the 80's, Lubotzky, Phillips and Sarnak applied the Ramanujan-Petersson Conjecture for $GL_{2}$ (Deligne's theorem), to a special family of arithmetic lattices, which act simply-transitively on the Bruhat-Tits trees
Externí odkaz:
http://arxiv.org/abs/1810.04710
Autor:
Parzanchevski, Ori
Ramanujan graphs have fascinating properties and history. In this paper we explore a parallel notion of Ramanujan digraphs, collecting relevant results from old and recent papers, and proving some new ones. Almost-normal Ramanujan digraphs are shown
Externí odkaz:
http://arxiv.org/abs/1804.08028
Autor:
Parzanchevski, Ori, Puder, Doron
Publikováno v:
Transactions of the American Mathematical Society, 373(10):7067-7086, 2020
Let $S_n$ denote the symmetric group on $n$ elements, and $\Sigma\subseteq S_{n}$ a symmetric subset of permutations. Aldous' spectral gap conjecture, proved by Caputo, Liggett and Richthammer [arXiv:0906.1238], states that if $\Sigma$ is a set of tr
Externí odkaz:
http://arxiv.org/abs/1804.02776
Autor:
Parzanchevski, Ori, Sarnak, Peter
Publikováno v:
Advances in Mathematics, Special volume honoring David Kazhdan, 327:869-901, 2018
To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of optimal strong
Externí odkaz:
http://arxiv.org/abs/1704.02106