In recent years, monotone double Hurwitz numbers were introduced as a naturally combinatorial modification of double Hurwitz numbers. Monotone double Hurwitz numbers share many structural properties with their classical counterparts, such as piecewise polynomiality, while the quantitative properties of these two numbers are quite different. We consider real analogues of monotone double Hurwitz numbers and study the asymptotics for these real analogues. The key ingredient is an interpretation of real tropical covers with arbitrary splittings as factorizations in the symmetric group which generalizes the result from Guay-Paquet et al. (2016) [18]. By using the above interpretation, we consider three types of real analogues of monotone double Hurwitz numbers: real monotone double Hurwitz numbers relative to simple splittings, relative to arbitrary splittings and real mixed double Hurwitz numbers. Under certain conditions, we find lower bounds for these real analogues, and obtain logarithmic asymptotics for real monotone double Hurwitz numbers relative to arbitrary splittings and real mixed double Hurwitz numbers. In particular, under given conditions real mixed double Hurwitz numbers are logarithmically equivalent to complex double Hurwitz numbers. We construct a family of real tropical covers and use them to show that real monotone double Hurwitz numbers relative to simple splittings are logarithmically equivalent to monotone double Hurwitz numbers with specific conditions. This is consistent with the logarithmic equivalence of real double Hurwitz numbers and complex double Hurwitz numbers.

近年来，单调双赫尔维茨数被引入作为双赫尔维茨数的自然组合修改。单调双赫维茨数与其经典对应数共享许多结构特性，例如分段多项式，而这两个数的定量特性却截然不同。我们考虑单调双赫维茨数的实数类似物并研究这些实数类似物的渐近性。关键要素是对真实热带覆盖物的解释，将任意分裂作为对称群中的因式分解，这概括了 Guay-Paquet 等人的结果。（2016） [18]。通过使用上述解释，我们考虑单调双赫维茨数的三种类型的实类比：相对于简单分裂的实单调双赫维兹数、相对于任意分裂的实单调双赫维兹数和实混合双赫维兹数。在某些条件下，我们找到这些实类似物的下界，并获得实单调双 Hurwitz 数相对于任意分裂和实混合双 Hurwitz 数的对数渐近。特别是，在给定条件下，实混合双赫尔维茨数在对数上等价于复双赫尔维茨数。我们构建了一个真实的热带覆盖族，并用它们来证明相对于简单分裂的真实单调双赫维兹数在对数上等价于特定条件下的单调双赫维兹数。这与实双赫尔维茨数和复双赫尔维茨数的对数等价一致。