We prove that the Maskin monotonicity⁎ condition (proposed by Bergemann et al. (2011)) fully characterizes exact rationalizable implementation in an environment with lotteries and transfers. ...Different from previous papers, our approach possesses many appealing features simultaneously, e.g., finite mechanisms with no integer game or modulo game are used; no transfers are made in any rationalizable profile; the message space is small; the implementation is robust to information perturbations in the sense of Oury and Tercieux (2012).
In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related ...to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.
Motion of Lee–Yang Zeros Hou, Qi; Jiang, Jianping; Newman, Charles M.
Journal of statistical physics,
03/2023, Letnik:
190, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive ...interactions is connected, we vary the interaction (denoted by
t
) at a fixed edge. It is already known that each zero is monotonic (either increasing or decreasing) in
t
; we prove that its motion is local: the entire trajectories of any two distinct zeros are disjoint. If the underlying graph is a complete graph and all interactions take the same value
t
≥
0
(i.e., the Curie-Weiss model), we prove that all the principal zeros (those in
i
0
,
π
/
2
)
) decrease strictly in
t
.
Quantum-mechanical wave–particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to ...self-interference—e.g., on transit across a double slit—for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability—in accord with available experimental evidence on the single- and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishability of the particles. This observation opens perspectives for the experimental characterization of many-particle coherence and sheds light on decoherence processes in many-particle systems.
We develop a sliding method for the nonlocal Monge–Ampère operator. We first establish a narrow region principle in bounded domains, which plays an important role in the sliding method. Then we ...consider the equation with the nonlocal Monge–Ampère operator and derive the monotonicity of solutions in both bounded domains and the whole space. We use a new idea-estimating the singular integrals defining the nonlocal Monge–Ampère operator along a sequence of approximate maximum points.
•We study the problem of sharing the revenues from broadcasting.•We consider several axioms based on the principle of monotonicity.•We provide axiomatic characterizations of rules with such ...axioms.•Our results highlight the normative appeal of the equal-split rule.
We explore the implications of the principle of monotonicity in the problem of sharing the revenues from broadcasting sports leagues. We formalize different forms of this principle as several axioms for sharing rules in this setting. We show that, combined with two other basic axioms (equal treatment of equals and additivity), they provide axiomatic characterizations of focal rules for this problem, as well as families of rules compromising among them. These results highlight the normative appeal of the (focal) equal-split rule.
In this paper, we study the asymptotic behavior of positive solutions of the fractional Hardy-Hénon equation(−Δ)σu=|x|αupinB1\{0} with an isolated singularity at the origin, where σ∈(0,1) and the ...punctured unit ball B1\{0}⊂Rn with n≥2. When −2σ<α<2σ and n+αn−2σ<p<n+2σn−2σ, we give a classification of isolated singularities of positive solutions, and in particular, this implies sharp blow up estimates of singular solutions. Further, we describe the precise asymptotic behavior of solutions near the singularity. More generally, we classify isolated boundary singularities and describe the precise asymptotic behavior of singular solutions for a relevant degenerate elliptic equation with a nonlinear Neumann boundary condition. These results parallel those known for the Laplacian counterpart proved by Gidas and Spruck (1981) 21, but the methods are very different, since the ODEs analysis is a missing ingredient in the fractional case. Our proofs are based on a monotonicity formula, combined with blow up (down) arguments, Kelvin transformation and uniqueness of solutions of related degenerate equations on S+n. We also investigate isolated singularities located at infinity of fractional Hardy-Hénon equations.
In this note, we present a unified approach to the problem of existence of a potential for the optimal transport problem with respect to non-traditional cost functions, that is costs that assume ...infinite values. We establish a new method which relies on proving solvability of a special (possibly infinite) family of linear inequalities. We give a necessary and sufficient condition on the coefficients that assure the existence of a solution, and which in the setting of transport theory we call c-path-boundedness. This condition fully characterizes sets that admit a potential and replaces c-cyclic monotonicity from the classical theory, i.e. when the cost is real-valued. Our method also gives a new and elementary proof for the classical results of Rockafellar, Rochet and Rüschendorf.
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