We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of “second order freeness” and interpret the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for second order freeness. By introducing cyclic Fock space, we also give an operator algebraic model fo...

In order to improve precision and efficiency sharing analysis should track both freeness and linearity. The abstract unification algorithms for these combined domains are suboptimal, hence there is scope for improving precision. This paper proposes three optimisations for tracing sharing in combination with freeness and linearity. A novel connection between equations and sharing abstractions is...

We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of these rules. We provide a combinatorial interpretation for partial freeness as the presence of closed paths in Hilbert space defined by particular joint moments....

We show that an asymptotic envy-freeness condition is necessary for a form of robust approximate implementation in large economies. In settings where agents’ allocations can be made excludably, asymptotic envy-freeness is also sufficient for implementation, while in nonexcludable settings it is not sufficient. ∗We are grateful for financial support from the National Science Foundation under gra...

The collaborative business process can be unreliable when business partners collaborate in a peer-to-peer fashion without central control. Therefore, an important issue that needs to be dealt with for any generic solution to manage collaborative business transaction is reliability verification. In this paper, we propose a novel Choreographical Business Transaction Net (CoBTx-Net) to specify col...

A sequence f : {1, . . . , n} → R contains a permutation π of length k if there exist i1 < . . . < ik such that f(ix) < f(iy) iff π(x) < π(y); otherwise, f is said to be π-free. As a simple special case, f is weakly monotone increasing iff it is (2, 1)-free. The problem of (one-sided) testing π-freeness in a sequence (or equivalently, efficiently finding a π-copy in a sequence far from π-freene...

We address the problem of approximating the distance of sparse graphs from having some predefined property P. The distance of G from having P is εP(G) if the minimum number of edge modifications needed in order to enforce P on G is εP(G) · m̄, where m̄ is an upper bound on the number of edges in the graph. When dealing with bounded-degree graphs of maximal degree d we take m̄ = dn, where n is the ...

We investigate the query complexity of fair allocation indivisible goods. For two agents with arbitrary monotonic utilities, we design an algorithm that computes satisfying envy-freeness up to one good (EF1), a relaxation envy-freeness, using logarithmic number queries. show bound also holds for three additive and polylogarithmic utilities. These results suggest it is possible fairly allocate g...

We prove effective base point freeness of the adjoint linear system on normal surfaces with a boundary.

Collaborative business process can become unreliable when business partners collaborate in a peerbased fashion without central control. Therefore, reliability checking becomes an important issue that needs to be dealt with for any generic solution in managing business collaboration. In this paper, we propose a novel Choreographical Business Transaction Net (CoBTx-Net) to model collaborative bus...