scholarly journals Random product of quasi-periodic cocycles

2020 ◽  
pp. 1
Author(s):  
Jamerson Bezerra ◽  
Mauricio Poletti
Keyword(s):  
Random Product

scholarly journals Tails of Stopped Random Products: The Factoid and Some Relatives

2008 ◽  
Vol 45 (04) ◽  
pp. 1161-1180
Author(s):  
Anthony G. Pakes
Keyword(s):  
Tail Behaviour ◽  
Random Product ◽  
Random Products ◽  
Heavy Tailed ◽  
First Time ◽  
Independent And Identically Distributed

The upper tail behaviour is explored for a stopped random product ∏j=1NXj, where the factors are positive and independent and identically distributed, andNis the first time one of the factors occupies a subset of the positive reals. This structure is motivated by a heavy-tailed analogue of the factorialn!, called the factoid ofn. Properties of the factoid suggested by computer explorations are shown to be valid. Two topics about the determination of the Zipf exponent in the rank-size law for city sizes are discussed.

scholarly journals Lyapunov Exponents for the Random Product of Two Shears

2018 ◽  
Vol 29 (2) ◽  
pp. 593-620 ◽  
Author(s):  
Rob Sturman ◽  
Jean-Luc Thiffeault
Keyword(s):  
Lyapunov Exponents ◽  
Random Product

scholarly journals Infinite Series of Singularities in the Correlated Random Matrices Product

2021 ◽  
Vol 9 ◽  
Author(s):  
Ruben Poghosyan ◽  
David B. Saakian
Keyword(s):  
Infinite Series ◽  
Transition Probabilities ◽  
Initial Vector ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Matrix ◽  
Previous Round ◽  
Random Product ◽  
Transition Points ◽  
Product Of Matrices

We consider the product of a large number of two 2 × 2 matrices chosen randomly (with some correlation): at any round there are transition probabilities for the matrix type, depending on the choice at previous round. Previously, a functional equation has been derived to calculate such a random product of matrices. Here, we identify the phase structure of the problem with exact expressions for the transition points separating “localized” and “ergodic” regimes. We demonstrate that the latter regime develops through a formation of an infinite series of singularities in the steady-state distribution of vectors that results from the action of the random product of matrices on an initial vector.

scholarly journals Concentration for Random Product Formulas

PRX Quantum ◽  
2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Chi-Fang Chen ◽  
Hsin-Yuan Huang ◽  
Richard Kueng ◽  
Joel A. Tropp
Keyword(s):  
Random Product ◽  
Product Formulas

scholarly journals Optimization of Warehouse Operations with Genetic Algorithms

2020 ◽  
Vol 10 (14) ◽  
pp. 4817
Author(s):  
Mirosław Kordos ◽  
Jan Boryczko ◽  
Marcin Blachnik ◽  
Sławomir Golak
Keyword(s):  
Genetic Algorithms ◽  
Product Placement ◽  
Order Picking ◽  
Crossover Operator ◽  
Proper Number ◽  
Random Product ◽  
Fully Automatic ◽  
The Cost ◽  
The Given ◽  
Warehouse Operations

We present a complete, fully automatic solution based on genetic algorithms for the optimization of discrete product placement and of order picking routes in a warehouse. The solution takes as input the warehouse structure and the list of orders and returns the optimized product placement, which minimizes the sum of the order picking times. The order picking routes are optimized mostly by genetic algorithms with multi-parent crossover operator, but for some cases also permutations and local search methods can be used. The product placement is optimized by another genetic algorithm, where the sum of the lengths of the optimized order picking routes is used as the cost of the given product placement. We present several ideas, which improve and accelerate the optimization, as the proper number of parents in crossover, the caching procedure, multiple restart and order grouping. In the presented experiments, in comparison with the random product placement and random product picking order, the optimization of order picking routes allowed the decrease of the total order picking times to 54%, optimization of product placement with the basic version of the method allowed to reduce that time to 26% and optimization of product placement with the methods with the improvements, as multiple restart and multi-parent crossover to 21%.

scholarly journals Random products of maps synchronizing on average

2020 ◽  
Vol 22 (08) ◽  
pp. 1950086
Author(s):  
Edgar Matias ◽  
Ítalo Melo
Keyword(s):  
Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Metric Space ◽  
Random Product ◽  
Random Products ◽  
Necessary And Sufficient

We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.

scholarly journals Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics

2020 ◽  
Vol 9 (6) ◽  
Author(s):  
Shiyu Zhou ◽  
Zhicheng Yang ◽  
Alioscia Hamma ◽  
Claudio Chamon
Keyword(s):  
Entanglement Entropy ◽  
Finite Size ◽  
Scaling Analysis ◽  
Product State ◽  
Finite Size Scaling ◽  
Level Spacing ◽  
Entanglement Spectrum ◽  
Universal Quantum ◽  
Random Product ◽  
Universal Gates

Clifford circuits are insufficient for universal quantum computation or creating tt-designs with t\ge 4t≥4. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8)(π/8) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.

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