All reports by Author Dor Minzer:

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TR20-009
| 6th February 2020
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Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra#### Theorems of KKL, Friedgut, and Talagrand via Random Restrictions and Log-Sobolev Inequality

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TR19-141
| 22nd October 2019
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Mark Braverman, Subhash Khot, Dor Minzer#### On Rich $2$-to-$1$ Games

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TR18-078
| 23rd April 2018
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Subhash Khot, Dor Minzer, Dana Moshkovitz, Muli Safra#### Small Set Expansion in The Johnson Graph

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TR18-006
| 10th January 2018
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Subhash Khot, Dor Minzer, Muli Safra#### Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion

Revisions: 2

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TR17-094
| 25th May 2017
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Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra#### On Non-Optimally Expanding Sets in Grassmann Graphs

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TR16-198
| 14th December 2016
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Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra#### Towards a Proof of the 2-to-1 Games Conjecture?

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TR15-011
| 22nd January 2015
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Subhash Khot, Dor Minzer, Muli Safra#### On Monotonicity Testing and Boolean Isoperimetric type Theorems

Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

We give alternate proofs for three related results in analysis of Boolean functions, namely the KKL

Theorem, Friedgutâ€™s Junta Theorem, and Talagrandâ€™s strengthening of the KKL Theorem. We follow a

new approach: looking at the first Fourier level of the function after a suitable random restriction and

applying the Log-Sobolev ...
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Mark Braverman, Subhash Khot, Dor Minzer

We propose a variant of the $2$-to-$1$ Games Conjecture that we call the Rich $2$-to-$1$ Games Conjecture and show that it is equivalent to the Unique Games Conjecture. We are motivated by two considerations. Firstly, in light of the recent proof of the $2$-to-$1$ Games Conjecture, we hope to understand ... more >>>

Subhash Khot, Dor Minzer, Dana Moshkovitz, Muli Safra

This paper studies expansion properties of the (generalized) Johnson Graph. For natural numbers

t < l < k, the nodes of the graph are sets of size l in a universe of size k. Two sets are connected if

their intersection is of size t. The Johnson graph arises often ...
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Subhash Khot, Dor Minzer, Muli Safra

We prove that pseudorandom sets in Grassmann graph have near-perfect expansion as hypothesized in [DKKMS-2]. This completes

the proof of the $2$-to-$2$ Games Conjecture (albeit with imperfect completeness) as proposed in [KMS, DKKMS-1], along with a

contribution from [BKT].

The Grassmann graph $Gr_{global}$ contains induced subgraphs $Gr_{local}$ that are themselves ... more >>>

Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

The paper investigates expansion properties of the Grassmann graph,

motivated by recent results of [KMS, DKKMS] concerning hardness

of the Vertex-Cover and of the $2$-to-$1$ Games problems. Proving the

hypotheses put forward by these papers seems to first require a better

understanding of these expansion properties.

We consider the edge ... more >>>

Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

We propose a combinatorial hypothesis regarding a subspace vs. subspace agreement test, and prove that if correct it leads to a proof of the 2-to-1 Games Conjecture, albeit with imperfect completeness.

Subhash Khot, Dor Minzer, Muli Safra

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we

give a monotonicity testing algorithm that makes $\tilde{O}(\sqrt{n}/\epsilon^2)$ non-adaptive queries to a function

$f:\{0,1\}^n \mapsto \{0,1\}$, always accepts a monotone function and rejects a function that is $\epsilon$-far from

being monotone ...
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