A tangent method derivation of the arctic curve for q -weighted paths with arbitrary starting points
A tangent method derivation of the arctic curve for q -weighted paths with arbitrary starting points
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任意起始点 q 加权路径的北极曲线的正切法推导
DOI：
10.1088/1751-8121/ab03ff
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Guitter, Emmanuel
中科院分区：
文献类型：
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作者：
Di Francesco, Philippe;Guitter, Emmanuel
我们使用切线方法的方法来获得北极曲线在第一象限内的非相交的晶格路径的模型，包括一个q依赖的权重与由路径界定的区域。我们的模型的特点是任意序列的起点沿着正水平轴，其分布涉及一个任意的分段可微函数。我们给出了一个明确的表达式北极曲线在这个任意函数和参数q。特别强调的是北极曲线的变形时，不同的q，并在其极限形状时，q趋于0或无穷大。我们的分析结果说明了一些详细的例子。
We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a q-dependent weight associated with the area delimited by the paths. Our model is characterized by an arbitrary sequence of starting points along the positive horizontal axis, whose distribution involves an arbitrary piecewise differentiable function. We give an explicit expression for the arctic curve in terms of this arbitrary function and of the parameter q. A particular emphasis is put on the deformation of the arctic curve upon varying q, and on its limiting shapes when q tends to 0 or infinity. Our analytic results are illustrated by a number of detailed examples.