Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Dikstein, Yotam"'
A long standing problem asks whether every group is sofic, i.e., can be separated by almost-homomorphisms to the symmetric group $Sym(n)$. Similar problems have been asked with respect to almost-homomorphisms to the unitary group $U(n)$, equipped wit
Externí odkaz:
http://arxiv.org/abs/2410.02913
High dimensional expanders (HDXs) are a hypergraph generalization of expander graphs. They are extensively studied in the math and TCS communities due to their many applications. Like expander graphs, HDXs are especially interesting for applications
Externí odkaz:
http://arxiv.org/abs/2405.19191
Autor:
Dikstein, Yotam, Hopkins, Max
We prove optimal concentration of measure for lifted functions on high dimensional expanders (HDX). Let $X$ be a $k$-dimensional HDX. We show for any $i\leq k$ and $f:X(i)\to [0,1]$: \[\Pr_{s\in X(k)}\left[\left|\underset{{t\subseteq s}}{\mathbb{E}}[
Externí odkaz:
http://arxiv.org/abs/2404.10961
We solve the derandomized direct product testing question in the low acceptance regime, by constructing new high dimensional expanders that have no small connected covers. We show that our complexes have swap cocycle expansion, which allows us to ded
Externí odkaz:
http://arxiv.org/abs/2402.01078
We point out an error in the paper "Linear Time Encoding of LDPC Codes" (by Jin Lu and Jos\'e M. F. Moura, IEEE Trans). The paper claims to present a linear time encoding algorithm for every LDPC code. We present a family of counterexamples, and poin
Externí odkaz:
http://arxiv.org/abs/2312.16125
Autor:
Dikstein, Yotam, Dinur, Irit
We introduce and study swap cosystolic expansion, a new expansion property of simplicial complexes. We prove lower bounds for swap coboundary expansion of spherical buildings and use them to lower bound swap cosystolic expansion of the LSV Ramanujan
Externí odkaz:
http://arxiv.org/abs/2312.15325
Autor:
Dikstein, Yotam, Dinur, Irit
Given a family $X$ of subsets of $[n]$ and an ensemble of local functions $\{f_s:s\to\Sigma\; | \; s\in X\}$, an agreement test is a randomized property tester that is supposed to test whether there is some global function $G:[n]\to\Sigma$ such that
Externí odkaz:
http://arxiv.org/abs/2308.09582
Autor:
Dikstein, Yotam, Dinur, Irit
We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building of $SL_n(F
Externí odkaz:
http://arxiv.org/abs/2304.01608
Autor:
Dikstein, Yotam
We present a new construction of high dimensional expanders based on covering spaces of simplicial complexes. High dimensional expanders (HDXs) are hypergraph analogues of expander graphs. They have many uses in theoretical computer science, but unfo
Externí odkaz:
http://arxiv.org/abs/2211.13568
Twisted hypercubes are generalizations of the Boolean hypercube, obtained by iteratively connecting two instances of a graph by a uniformly random perfect matching. Dudek et al. showed that when the two instances are independent, these graphs have op
Externí odkaz:
http://arxiv.org/abs/2211.06988